🕷️ Crawler Inspector

URL Lookup

Direct Parameter Lookup

Raw Queries and Responses

1. Shard Calculation

Query:

Response:

Calculated Shard: 15 (from laksa102)

2. Crawled Status Check

Query:

curl -X POST \
  'http://laksa015.int.ahrefs:8124/' \
  -H 'Content-Type: text/plain' \
  -H 'X-ClickHouse-Database: crawler3' \
  -H 'Authorization: Basic YXBpOg==' \
  -d 'SELECT getAhrefsURLFromUnparsed(src_unparsed) AS found_url, ifNull(toUnixTimestamp(download_stamp), 0) AS crawl_time, ifNull(toUnixTimestamp(props_url_first_seen), 0) AS first_indexed_time, download_http_code AS http_code, src_unparsed AS src_unparsed, src_root_hash AS src_root_hash, history_drop_reason AS history_drop_reason, meta_title AS meta_title, meta_descriptions AS meta_descriptions, attrs_boilerpipe_text AS attrs_boilerpipe_text, attrs_markdown AS attrs_markdown, attrs_readable_markdown AS attrs_readable_markdown, meta_canonical AS meta_canonical FROM crawler3.page_info_local FINAL PREWHERE (src_root_hash, src_unparsed) IN ((getAhrefsRootHashFromUnparsed(getAhrefsUnparsedNoserviceFromURL(\'https://m.blog.naver.com/galaxyenergy/221090965396\')), getAhrefsUnparsedNoserviceFromURL(\'https://m.blog.naver.com/galaxyenergy/221090965396\'))) FORMAT JSONEachRow'

Response:

{"found_url":"https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396","crawl_time":1756177984,"first_indexed_time":0,"http_code":200,"src_unparsed":"com,naver!blog,m,\/galaxyenergy\/221090965396 s443","src_root_hash":"2598804620694055015","history_drop_reason":null,"meta_title":"등비수열 합 공식 원리 이해하기 : 네이버 블로그","meta_descriptions":[],"attrs_boilerpipe_text":"숫자들이 규칙적으로 늘어서 있을 때 152 째는 어떤 수가 나오느냐 ? 처음부터 152번째 수까지 모조리 다 합치면 얼마냐 ? 이런 파트가 수열이다","attrs_markdown":"![](https:\/\/ssl.pstatic.net\/static\/blog\/sp_blog72.png) ![](https:\/\/ssl.pstatic.net\/static\/blog\/sp_blog_se3_6.png)\n\n[본문 바로가기](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396#ct)\n\n# [블로그](https:\/\/m.blog.naver.com\/Recommendation.naver)\n## [카테고리 이동](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)     [Mathematicspalace](https:\/\/m.blog.naver.com\/PostList.naver?blogId=galaxyenergy)\n\n[검색](https:\/\/m.blog.naver.com\/PostSearchList.naver?blogId=galaxyenergy)\n\nMY메뉴 열기\n\n![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxNzA5MDZfNDAg\/MDAxNTA0Njk2OTI0NDg3.H2P11fpl71RUGnIKDGbVDKqaLnXyn_LiR8vLQONavkIg.LVnzBGCkDWgwZ7GdkNNOVzE_T7bYdbH4XXeWMt3hcP0g.PNG.galaxyenergy\/tumblr_inline_mx0fmh0IqI1qdmskj.png?type=w800)\n\n[중고수학](https:\/\/m.blog.naver.com\/PostList.naver?blogId=galaxyenergy&categoryNo=24&logCode=0&categoryName=%EC%A4%91%EA%B3%A0%EC%88%98%ED%95%99#postlist_block)\n\n### 등비수열 합 공식 원리 이해하기\n[![프로필](https:\/\/blogpfthumb-phinf.pstatic.net\/MjAyNTA3MjFfMjQ0\/MDAxNzUzMDIzNzUyMDYw.pBgHVHCI4wlIdl_dPcMH9RFlGbZbcnhoU2hsoOfqAdog.Ymsb1k-uAHsahcGN-uPIqde4iv6_8YTJFYbEMdqucKIg.JPEG\/profileImage.jpg?type=s1)](https:\/\/m.blog.naver.com\/PostList.naver?blogId=galaxyenergy)\n\n[**galaxyenergy**](https:\/\/m.blog.naver.com\/PostList.naver?blogId=galaxyenergy)\n\n2017\\. 9. 6. 20:45\n\n[이웃추가](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n본문 기타 기능\n\n- **본문 폰트 크기 조정**\n  본문 폰트 크기 작게 보기\n  본문 폰트 크기 크게 보기\n  가\n- [공유하기](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n- [URL복사](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n- [신고하기](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n***수학에***  \n***수열이라는 파트가 있다***\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxNzA5MDZfNzUg\/MDAxNTA0Njk3MDAwNDU4.h44T4tQj_xzdoyS-F9ndbsQesaPN_DImYB6pjYUrb2Ag.nxJjdU1XfshvC4BtLTszLJYugAG8aAfPGqxA_NF1ghIg.JPEG.galaxyenergy\/downloadfile-64.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxNzA5MDZfMTQ2\/MDAxNTA0Njk2OTYxNTAz.u5n1n85dit8LIZc_b34Oy_5eBqU2rFDeymO6c2uGt0sg.kTH_S7avUoW4lLOHghSOCxvi-ohtQuUTYx_f4CfU50kg.JPEG.galaxyenergy\/downloadfile-341.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n***숫자들이***  \n***규칙적으로 늘어서 있을 때***  \n  \n***152 째는 어떤 수가 나오느냐 ?***  \n  \n***처음부터 152번째 수까지***  \n***모조리 다 합치면 얼마냐 ?***  \n  \n***이런 파트가 수열이다***\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxNzA5MDZfNjYg\/MDAxNTA0Njk3MDQwNDQ3.FxrDALy4lxBQpXVtMU0IACPVwoH5KHKGtfNEKxemP14g.-BJu08cshW6LL5ptbRDVofYskWmxm1c60k4Qh68r3VAg.JPEG.galaxyenergy\/20170825_211027.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n***미적분 확률통계처럼***  \n***수열도***   \n***수학의 하나의 거대한 분야다***\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxNzA5MDZfMTM5\/MDAxNTA0Njk3MTA0OTkz.J8afEzgQ3jYj03WTu8sI6s1ML8nH7r7oB8c9nAPeF0sg.Q4KGfJJWDo8rLM4sUkygDZmB030kgenA-Mn7lVJF03Yg.JPEG.galaxyenergy\/1504697104328.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n**오늘은**  \n**수열의 최고의 기초핵심이랄 수 있는**  \n  \n***등비수열의 합에 관해***  \n ***알아보자***\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxODEyMjhfMjUy\/MDAxNTQ1OTc3MjgxMTYy.Ajt-UVDU9pGpcn9ZXCbmGj1p8jURT4HuNO_NIFNz2dkg.uUlgy1U2GeO4Y5oTQlL6X3bWAQhl1fa78C0d2mI_jQog.JPEG.galaxyenergy\/1545907084449.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxODEyMjhfODcg\/MDAxNTQ1OTc3MjgzMDgy.hkAL9KvjBHHCnrv01KshfnX12ONrsnB3rV1sdW6vCa8g.XloIXtRbm-VhXLHOLdxfUZjh8LUppqNXOgL2Ng8wtNIg.JPEG.galaxyenergy\/1545907124467.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxODEyMjhfMSAg\/MDAxNTQ1OTc3Mjg0OTYx.4WBHULpMIoGi04HYUXIuypt_hPEsO9EQDflVCHbVpv0g.N3-ZcrYEfXK2eHZH8bBOa2Ee1xVmq7Pb7oMpXxN_lqog.JPEG.galaxyenergy\/1545907143344.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxODEyMjhfMjUw\/MDAxNTQ1OTc3Mjg3MTIz.zpmuQAdUg2lVcn4_mtVfg4SKIXAqLh4ONQvh0d1qybYg.0GwUUMARix-YFwnu2alWxFsGdJw8dSEL_gZ98iSa95Ag.JPEG.galaxyenergy\/18-12-27-19-43-10-274_deco.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxNzA5MDZfMTQg\/MDAxNTA0Njk3MTg3ODk0.CaAGmur8QmL4XhwUnIKyfa4CDXPYkVM3sT1zQZveZW4g.mJIj6jfYz3NnLRs-W_ihzaEQEFVKl6vescHEwsJrh4Ig.PNG.galaxyenergy\/pixiv52426657_4.png?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxOTA2MTRfMjQy\/MDAxNTYwNTA4NTg3MzIx.zcnvfBOFlwfjELnkwQctkh3trHlez9Sp8mjaBKOuqAUg.-NVn0DiPHz98GdzJsBVDQzW4ji8pmkttlRsz4vpA92og.JPEG.galaxyenergy\/1560495390510.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxOTA2MTRfMTY3\/MDAxNTYwNTA4NTg4NTU5.2FMJr-N1JlYlkjB3FOTtZ1xo1hlF-a4bYnuGl-4hiVYg.y_gLkgVABQRgTtGT6MqfWMdYM866BILUZFgz63qL92Ag.JPEG.galaxyenergy\/19-06-14-15-35-10-462_deco.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxOTA2MTRfMTk2\/MDAxNTYwNTA4NTg5NzMw.EChFBMmfHQwKLwHuGMfBOgKvewnlKElpQ0w6lV9eqM8g.OFinamhNyjyt0saWaHcdyi5rket5tixl1YW4PD_71Cog.JPEG.galaxyenergy\/19-06-14-16-13-53-674_deco.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxOTA2MTRfMjM5\/MDAxNTYwNTA4NTkxMTY3.C7hUs4v302ocok35j1ehBT9MdpNfZrQpfnQPS4t7tHQg.GP1ZJT3acGEVhWemexbr-7pR_JokE24SokYjjDnzZB0g.JPEG.galaxyenergy\/19-06-14-16-14-35-305_deco.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxNzA5MDZfOTAg\/MDAxNTA0Njk3MjE1Nzg0.3MGtpKrDq_xl6L-HshMRoXj6TnFcpvS7C2h79xDyLGsg.PAVWibMeinNDjLjET2-f4T5l0yTEha0IKgB1oICdfSgg.JPEG.galaxyenergy\/20170906_195334.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n***등비수열이란 뭐냐 하면***  \n***저런 걸 등비수열이라고 한다***\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxNzA5MDZfMjU4\/MDAxNTA0Njk3MjMzNjEy.5AGe787voAiUyVa3Q1ZOl62sURHx90_eqSSV2xTluNUg.l89S5A07dbG6rqL1UlM8kxI7fVyeAIXapfftfZZt9hMg.JPEG.galaxyenergy\/20170906_195417.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n***저렇게 계속 용돈을 받을 경우***  \n  \n***\"87달째는 얼마의 용돈을 받느냐\"***  \n***그것을***  \n***구하는 것을 등비수열의 일반항***  \n  \n***\"첫달부터 87달째까지***  \n***용돈을 모두 다 합치면 얼마냐 \"***  \n***그것을***  \n***구하는 것을 등비수열의 합이라고 한다***\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxNzA5MDZfMTYg\/MDAxNTA0Njk3NDQ2NTQz.6pS5NeetbQKEm6YoelEJkaj1ZFpQbYF8McZIuCCV7kQg.8JQ18GLCsbucAfAszgLte96IMt2ybWJMqwUb22HvFzwg.JPEG.galaxyenergy\/Ami-Mizuno-sailor-mercury-28226571-500-388.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxNzA5MDZfNjQg\/MDAxNTA0Njk3NDc1NzIw.DXvvknRSFV8TjxsO-XushNB958wK-7YdGziwDlKRK_Mg.9woWfG2L7SkVjD5uCZNNfXMJaeV6WnEUTIjPXwJkzbwg.PNG.galaxyenergy\/20170906_203003.png?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxNzA5MDZfMjk3\/MDAxNTA0Njk3NDc2MjUy.OIiWJaUAsLVkOmz6q2_qv3INP5_cvxRRGgS45Xkb_64g.1btrhXgI-IirugqH5t3u0vLLTQ-EnhOv9hXbmaXSkyYg.JPEG.galaxyenergy\/1504697104328.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n***일반항이건 합이건***  \n***공식이 있어***  \n***공식에 숫자만 집어넣으면 답이 나온다***  \n  \n***등비수열의 합을***  \n***공식을 모른다 치고 구해 보자***\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxNzA5MDZfMzQg\/MDAxNTA0Njk3NTA2MDE2.qY75dq7Om7ervf1dbenNVvlzP5oD058NP_diaOQJMeQg.bXVf1XP855o5fq4Y5dAVScvjpVDDuMAiBvhiJVGMjVYg.JPEG.galaxyenergy\/5-018-140rei.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxNzA5MDZfMTcg\/MDAxNTA0Njk3NTM4NTMw.j-grs2E7XnufEyqh3JJT9UNX6DxawnYZ2hKZ-Y_UGqsg.r_mqJxD1Sc3GFKARhm0n9GfNCpjesWqv88KOJuV-kKQg.JPEG.galaxyenergy\/20170906_194633.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n***다음과 같은***  \n***101 개의 숫자들을***  \n***몽땅 합치면***   \n  \n***그 합은 얼마냐 ?***  \n  \n***이것을 등비수열의 합이라고 한다***\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxNzA5MDZfMjI3\/MDAxNTA0NzA5MTkzNzE4.hi83DzhZvf4inaai4lXvBuofVTCVjaTI8jZu9Ule17Yg.ufAMfD642Zh8zjDX7F9UZ68RN4YKRFkQQ-zEuMMi_Jcg.JPEG.galaxyenergy\/20170906_194720.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n***자세히 보면***  \n***개수는 모두 101 개다***  \n  \n***이 101 개라는 개수를***  \n***항수 혹은 n 이라고 한다***\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxNzA5MDZfNzMg\/MDAxNTA0Njk3NjI2NDEw.VKzLCnQRGyAFZzPzciwL_59Q75lOvE_VSHdVK-2Li5wg.pNWujrQ_Zqxl6DtO5c5Uf2WTHb9-ELPXL_OQc8qDuM4g.JPEG.galaxyenergy\/20170906_194655.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n***이 숫자들이 늘어선 규칙은***  \n  \n***(항상 앞의 것에 ×2 하면 뒤의 것이다)***  \n  \n***2를***   \n***공비 혹은 r 이라고 한다***\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxNzA5MDZfMTk3\/MDAxNTA0Njk3NjYzMDM0.40Fj14UhgnPekdXhnG2VxU16cnDxs_-buq7s8t0u5oQg.1ZDu-dvYC_yl28WfZgQqodq9v0NH96_8AXqpq79lEhgg.JPEG.galaxyenergy\/17-09-06-19-43-47-562_deco.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n***그리고***  \n***맨 앞에 있는 저것을***  \n ***초항 혹은 a라고 한다***  \n***(여기서는 1을 가리킨다)***\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxNzA5MDZfMTcw\/MDAxNTA0Njk3Njg1MzA3.FtlHjasDyVQ1r47_oU3C5LXMm6lYsMk48vpb2bkAPbAg.JJ1fhrhLD8in9EK7bkm6ak-SjXKYjXujX1WG87UILf8g.JPEG.galaxyenergy\/1504697104328.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n***저 101 개의 숫자들의 합을 구하는***  \n***공식이 있는데***  \n  \n***공식을 모른다 가정하고 구해보자***\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxNzA5MDZfMjkx\/MDAxNTA0Njk3NzAwNDc3.Uaxrv2HDzBFbd9B81B-9r_5wA5gfOdxhdfF5XJtFcy8g.HgiTsVkPJo-9VHZRABRfBm5YlGH6TDyBihHuRCSkNK0g.JPEG.galaxyenergy\/20170906_194633.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n***일단***  \n***몽땅 합친 것을 S라고 하자***  \n***(S를 구하는 것이 목적이다)***  \n  \n***저 101 개의 숫자들을***  \n***하나하나 합쳐서 전체 합을 구하는 것은***   \n***미친 짓이다***  \n  \n***수학적 테크닉과 기교를 사용해야 한다***\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxNzA5MDZfMjAz\/MDAxNTA0Njk3ODAyMTgx.SgKw2X3LN7LTEpY0Vi55rroNOeLYP6QrICbn-NUj88Ug.j4ogjhx1tNA1ltGLZrtBuet-MByiy2UmOELL3ZVwg_4g.JPEG.galaxyenergy\/1504697782868.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n***S에***   \n***공비 2를 곱해서***  \n***2S라는 새로운 식을 만든다***\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxNzA5MDZfMTc5\/MDAxNTA0Njk3ODMwODgy.qEElsoVSR5644gnhqy1o3HhtSbHlCWP3cELjpxKA8GMg.UkSPEDWMgcG6r8ZQDPo85Hmfa1XYIibA-DlQRKKdhcgg.JPEG.galaxyenergy\/1504697829750.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n***그 다음***  \n***2S에서 S를 빼준다***  \n  \n***그러면 빼주는 과정에서***  \n***같은 것끼리는 다 지워지고***  \n***딱 두 개만 남는다***\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxNzA5MDZfMjE4\/MDAxNTA0Njk3ODg2NjYz.uoWUhIqKFovNW_pAFsXLlNct0V__HjIHO-2zdggFDuUg.EVPoOlWJD9vq5S0vEqyfo-pPkH2sTttgTZ6PE9HuDCMg.JPEG.galaxyenergy\/1504697883943.jpg?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n***그것이 답이다***\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxNzA5MDZfMTI1\/MDAxNTA0Njk3OTA4MjE3.NaL6e7BEpinPm62xjbCmtthElfZlr0VgjS_0Y7djNngg.dzHXWKvYM24-In68FK6prQiaFa_ezehiqpt1g8HroOYg.PNG.galaxyenergy\/3-1.png?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n***사실은 이것이***  \n***등비수열의 합공식을 만드는***  \n***과정이기도 하다***\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxNzA5MDZfMjMz\/MDAxNTA0Njk3OTI0OTY0.zjhd3N4pZ7BIT7ZdZm0L-vtrFxKNMtL3-UvaYC5Zkn0g.FgS2IFaQZxMrqSY0wq5NP2CwgSO4CVAHnvISEfvyz0Yg.PNG.galaxyenergy\/20170906_201840.png?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n[![](https:\/\/mblogthumb-phinf.pstatic.net\/MjAxNzA5MDZfMjQw\/MDAxNTA0Njk4MDEwNTMx.seAVCI42SFXCghwK1oitQZThURWw_571hHBngwDNvmkg.qTr2n4J9gEins4jAH7SAPP8_rwYi_HpZnLupfiDHb6Yg.PNG.galaxyenergy\/20170828_161457.png?type=w80_blur)](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n[![](https:\/\/dthumb-phinf.pstatic.net\/?src=%22https%3A%2F%2Fblogthumb.pstatic.net%2FMjAxOTA2MTFfNzYg%2FMDAxNTYwMjM3MjY0NzEy.DVBcX4On0B0qxPtP-tri4OmixKC5bmNgx3Afw5-O18gg.L3eBJo-rPiESh-wvZYIx0A1yrFIFeJ2MCWTalN3E8sIg.JPEG.galaxyenergy%2F1546514456981.jpg%3Ftype%3Dw2%22&type=ff500_300) 미분 도함수 기하와 도형으로 이해하기 미분을 기하와 도형으로 이해해야 진정으로 미분을 이해한다고 할 수 있다 x²을 미분하면 2x 이런 식으로 ... m.blog.naver.com](https:\/\/m.blog.naver.com\/galaxyenergy\/221559554463)\n\n[![](https:\/\/dthumb-phinf.pstatic.net\/?src=%22https%3A%2F%2Fblogthumb.pstatic.net%2FMjAxOTA0MTFfMTgz%2FMDAxNTU0OTY0MjUzMjg1.eFC1trq-nmcJdkAWFO4X-nsvwb2t_k86KeJQ2sHfmRsg.pLTh6LwGKI_OrpG8XRTd1zgI-fAznYVvWK35xarMycIg.JPEG.galaxyenergy%2FBandPhoto_3169198329.jpg%3Ftype%3Dw2%22&type=ff500_300) 합성함수 미분 기하와 산수로 이해하기 합성함수 미분은 미적분의 최대의 키포인트다 (치환적분도 합성함수 미분의 역이다) y = (x³+ 5x²)⁴+ 6(x³... m.blog.naver.com](https:\/\/m.blog.naver.com\/galaxyenergy\/221511145415)\n\n[![](https:\/\/dthumb-phinf.pstatic.net\/?src=%22https%3A%2F%2Fblogthumb.pstatic.net%2FMjAxODExMzBfMjE2%2FMDAxNTQzNTc5MjEzMjU0.uU2cx8NfRTT7vPhIo6t3R_sfuVgLuAgCe-8SzTsSdXUg.BviFktwtlqH-eI9rpjXWJYMBKfT546NZHXvRgNZMVswg.JPEG.galaxyenergy%2FBandPhoto_3169198329.jpg%3Ftype%3Dw2%22&type=ff500_300) 합성함수 미분 연애와 키스 원리로 이해하기 합성함수 미분이란 함수의 한 점에서의 기울기를 (미분) 구하기 어려우니까 두 개의 기울기를 곱하는 방법... m.blog.naver.com](https:\/\/m.blog.naver.com\/galaxyenergy\/221409757973)\n\n[![](https:\/\/dthumb-phinf.pstatic.net\/?src=%22https%3A%2F%2Fblogthumb.pstatic.net%2FMjAxODExMjlfMjQw%2FMDAxNTQzNDkwNDQ0MDcz.PjXbQwEFoeeV45-mItW10wL3G6nk0dHS2pPJdibrkMIg.AXsFgYVRrqjPbf4OcbKJdX_lWg4YJYf3JrlC1JVm-60g.JPEG.galaxyenergy%2F1537009857598.jpg%3Ftype%3Dw2%22&type=ff120) 치환적분 기하와 도형으로 이해하기 치환적분 말뜻을 알고 고등학교 졸업한 사람은 100명 중 1명도 안 되고 대학교에서도 계속 두드려외운다 3x... m.blog.naver.com](https:\/\/m.blog.naver.com\/galaxyenergy\/221408975283)\n\n[![](https:\/\/dthumb-phinf.pstatic.net\/?src=%22https%3A%2F%2Fblogthumb.pstatic.net%2FMjAxODA2MjhfMyAg%2FMDAxNTMwMTg2MzMxMjQw.zMB6B__ixnS3opUM8um8dIXvIs02s8pdX9zhSF4rRF4g.xyuQQ1wbtTB30v7Wq7Rt-6bilAV9BWq-FoDzdl61hK8g.JPEG.galaxyenergy%2F1530184165865.jpg%3Ftype%3Dw2%22&type=ff500_300) 삼각비 삼각함수 일반각 단위원 종합적으로 이해하기 중학교 때는 (0 ° \\~~ 90°) 범위의 삼각함수만 다룬다 (그냥 삼각비라 부른다) 고등학교 때는 구간이 ( -∞ ... m.blog.naver.com](https:\/\/m.blog.naver.com\/galaxyenergy\/221308833389)\n\n[![](https:\/\/dthumb-phinf.pstatic.net\/?src=%22https%3A%2F%2Fblogthumb.pstatic.net%2FMjAxODAyMDJfMjAw%2FMDAxNTE3NTcyNjEwODM3.D9v3TJ-Azd84gm2aWpCSz1OqE8y5rPzGX3FT8csFmiog.fjSeHdqGZI9z0_ohwuaYZFkPqftH8PfgycWF6k2Uf_Qg.JPEG.galaxyenergy%2FBandPhoto_3169198329.jpg%3Ftype%3Dw2%22&type=ff500_300) 일반각 삼각함수 난해한 어려운 세계 가볍게 정복하기 정말 어려운 것이라서 고등학교 때는 그냥 무조건 외우고 무조건 외우는 그것조차 너무나 힘이 들어서 수학... 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합 공식 원리 이해하기\",\"source\":\"https:\/\/blog.naver.com\/galaxyenergy\/221090965396\",\"blogName\":\"Mathemati..\",\"domainIdOrBlogId\":\"galaxyenergy\",\"nicknameOrBlogId\":\"galaxyenergy\",\"logNo\":221090965396,\"smartEditorVersion\":3,\"meDisplay\":true,\"lineDisplay\":true,\"outsideDisplay\":true,\"cafeDisplay\":true,\"blogDisplay\":true}\n\n[닫기](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n## 카테고리\n[이 블로그 홈](https:\/\/m.blog.naver.com\/galaxyenergy)\n\n[공유하기](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)\n\n**galaxyenergy** 님을 이웃추가하고 새글을 받아보세요\n\n[취소](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396) [이웃추가](https:\/\/m.blog.naver.com\/galaxyenergy\/221090965396)","attrs_readable_markdown":null,"meta_canonical":null}

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URL	https://m.blog.naver.com/galaxyenergy/221090965396
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Meta Title	등비수열 합 공식 원리 이해하기 : 네이버 블로그
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Boilerpipe Text	숫자들이 규칙적으로 늘어서 있을 때 152 째는 어떤 수가 나오느냐 ? 처음부터 152번째 수까지 모조리 다 합치면 얼마냐 ? 이런 파트가 수열이다
Markdown	![](https://ssl.pstatic.net/static/blog/sp_blog72.png) ![](https://ssl.pstatic.net/static/blog/sp_blog_se3_6.png) [본문 바로가기](https://m.blog.naver.com/galaxyenergy/221090965396#ct) # [블로그](https://m.blog.naver.com/Recommendation.naver) ## [카테고리 이동](https://m.blog.naver.com/galaxyenergy/221090965396) [Mathematicspalace](https://m.blog.naver.com/PostList.naver?blogId=galaxyenergy) [검색](https://m.blog.naver.com/PostSearchList.naver?blogId=galaxyenergy) MY메뉴 열기 ![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfNDAg/MDAxNTA0Njk2OTI0NDg3.H2P11fpl71RUGnIKDGbVDKqaLnXyn_LiR8vLQONavkIg.LVnzBGCkDWgwZ7GdkNNOVzE_T7bYdbH4XXeWMt3hcP0g.PNG.galaxyenergy/tumblr_inline_mx0fmh0IqI1qdmskj.png?type=w800) [중고수학](https://m.blog.naver.com/PostList.naver?blogId=galaxyenergy&categoryNo=24&logCode=0&categoryName=%EC%A4%91%EA%B3%A0%EC%88%98%ED%95%99#postlist_block) ### 등비수열 합 공식 원리 이해하기 [![프로필](https://blogpfthumb-phinf.pstatic.net/MjAyNTA3MjFfMjQ0/MDAxNzUzMDIzNzUyMDYw.pBgHVHCI4wlIdl_dPcMH9RFlGbZbcnhoU2hsoOfqAdog.Ymsb1k-uAHsahcGN-uPIqde4iv6_8YTJFYbEMdqucKIg.JPEG/profileImage.jpg?type=s1)](https://m.blog.naver.com/PostList.naver?blogId=galaxyenergy) [galaxyenergy](https://m.blog.naver.com/PostList.naver?blogId=galaxyenergy) 2017\. 9. 6. 20:45 [이웃추가](https://m.blog.naver.com/galaxyenergy/221090965396) 본문 기타 기능 - 본문 폰트 크기 조정 본문 폰트 크기 작게 보기 본문 폰트 크기 크게 보기 가 - [공유하기](https://m.blog.naver.com/galaxyenergy/221090965396) - [URL복사](https://m.blog.naver.com/galaxyenergy/221090965396) - [신고하기](https://m.blog.naver.com/galaxyenergy/221090965396) *수학에* *수열이라는 파트가 있다* [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfNzUg/MDAxNTA0Njk3MDAwNDU4.h44T4tQj_xzdoyS-F9ndbsQesaPN_DImYB6pjYUrb2Ag.nxJjdU1XfshvC4BtLTszLJYugAG8aAfPGqxA_NF1ghIg.JPEG.galaxyenergy/downloadfile-64.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMTQ2/MDAxNTA0Njk2OTYxNTAz.u5n1n85dit8LIZc_b34Oy_5eBqU2rFDeymO6c2uGt0sg.kTH_S7avUoW4lLOHghSOCxvi-ohtQuUTYx_f4CfU50kg.JPEG.galaxyenergy/downloadfile-341.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) *숫자들이* *규칙적으로 늘어서 있을 때* *152 째는 어떤 수가 나오느냐 ?* *처음부터 152번째 수까지* *모조리 다 합치면 얼마냐 ?* *이런 파트가 수열이다* [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfNjYg/MDAxNTA0Njk3MDQwNDQ3.FxrDALy4lxBQpXVtMU0IACPVwoH5KHKGtfNEKxemP14g.-BJu08cshW6LL5ptbRDVofYskWmxm1c60k4Qh68r3VAg.JPEG.galaxyenergy/20170825_211027.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) *미적분 확률통계처럼* *수열도* *수학의 하나의 거대한 분야다* [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMTM5/MDAxNTA0Njk3MTA0OTkz.J8afEzgQ3jYj03WTu8sI6s1ML8nH7r7oB8c9nAPeF0sg.Q4KGfJJWDo8rLM4sUkygDZmB030kgenA-Mn7lVJF03Yg.JPEG.galaxyenergy/1504697104328.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) 오늘은 수열의 최고의 기초핵심이랄 수 있는 *등비수열의 합에 관해* *알아보자* [![](https://mblogthumb-phinf.pstatic.net/MjAxODEyMjhfMjUy/MDAxNTQ1OTc3MjgxMTYy.Ajt-UVDU9pGpcn9ZXCbmGj1p8jURT4HuNO_NIFNz2dkg.uUlgy1U2GeO4Y5oTQlL6X3bWAQhl1fa78C0d2mI_jQog.JPEG.galaxyenergy/1545907084449.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxODEyMjhfODcg/MDAxNTQ1OTc3MjgzMDgy.hkAL9KvjBHHCnrv01KshfnX12ONrsnB3rV1sdW6vCa8g.XloIXtRbm-VhXLHOLdxfUZjh8LUppqNXOgL2Ng8wtNIg.JPEG.galaxyenergy/1545907124467.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxODEyMjhfMSAg/MDAxNTQ1OTc3Mjg0OTYx.4WBHULpMIoGi04HYUXIuypt_hPEsO9EQDflVCHbVpv0g.N3-ZcrYEfXK2eHZH8bBOa2Ee1xVmq7Pb7oMpXxN_lqog.JPEG.galaxyenergy/1545907143344.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxODEyMjhfMjUw/MDAxNTQ1OTc3Mjg3MTIz.zpmuQAdUg2lVcn4_mtVfg4SKIXAqLh4ONQvh0d1qybYg.0GwUUMARix-YFwnu2alWxFsGdJw8dSEL_gZ98iSa95Ag.JPEG.galaxyenergy/18-12-27-19-43-10-274_deco.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMTQg/MDAxNTA0Njk3MTg3ODk0.CaAGmur8QmL4XhwUnIKyfa4CDXPYkVM3sT1zQZveZW4g.mJIj6jfYz3NnLRs-W_ihzaEQEFVKl6vescHEwsJrh4Ig.PNG.galaxyenergy/pixiv52426657_4.png?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxOTA2MTRfMjQy/MDAxNTYwNTA4NTg3MzIx.zcnvfBOFlwfjELnkwQctkh3trHlez9Sp8mjaBKOuqAUg.-NVn0DiPHz98GdzJsBVDQzW4ji8pmkttlRsz4vpA92og.JPEG.galaxyenergy/1560495390510.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxOTA2MTRfMTY3/MDAxNTYwNTA4NTg4NTU5.2FMJr-N1JlYlkjB3FOTtZ1xo1hlF-a4bYnuGl-4hiVYg.y_gLkgVABQRgTtGT6MqfWMdYM866BILUZFgz63qL92Ag.JPEG.galaxyenergy/19-06-14-15-35-10-462_deco.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxOTA2MTRfMTk2/MDAxNTYwNTA4NTg5NzMw.EChFBMmfHQwKLwHuGMfBOgKvewnlKElpQ0w6lV9eqM8g.OFinamhNyjyt0saWaHcdyi5rket5tixl1YW4PD_71Cog.JPEG.galaxyenergy/19-06-14-16-13-53-674_deco.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxOTA2MTRfMjM5/MDAxNTYwNTA4NTkxMTY3.C7hUs4v302ocok35j1ehBT9MdpNfZrQpfnQPS4t7tHQg.GP1ZJT3acGEVhWemexbr-7pR_JokE24SokYjjDnzZB0g.JPEG.galaxyenergy/19-06-14-16-14-35-305_deco.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfOTAg/MDAxNTA0Njk3MjE1Nzg0.3MGtpKrDq_xl6L-HshMRoXj6TnFcpvS7C2h79xDyLGsg.PAVWibMeinNDjLjET2-f4T5l0yTEha0IKgB1oICdfSgg.JPEG.galaxyenergy/20170906_195334.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) *등비수열이란 뭐냐 하면* *저런 걸 등비수열이라고 한다* [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMjU4/MDAxNTA0Njk3MjMzNjEy.5AGe787voAiUyVa3Q1ZOl62sURHx90_eqSSV2xTluNUg.l89S5A07dbG6rqL1UlM8kxI7fVyeAIXapfftfZZt9hMg.JPEG.galaxyenergy/20170906_195417.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) *저렇게 계속 용돈을 받을 경우* *"87달째는 얼마의 용돈을 받느냐"* *그것을* *구하는 것을 등비수열의 일반항* *"첫달부터 87달째까지* *용돈을 모두 다 합치면 얼마냐 "* *그것을* *구하는 것을 등비수열의 합이라고 한다* [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMTYg/MDAxNTA0Njk3NDQ2NTQz.6pS5NeetbQKEm6YoelEJkaj1ZFpQbYF8McZIuCCV7kQg.8JQ18GLCsbucAfAszgLte96IMt2ybWJMqwUb22HvFzwg.JPEG.galaxyenergy/Ami-Mizuno-sailor-mercury-28226571-500-388.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfNjQg/MDAxNTA0Njk3NDc1NzIw.DXvvknRSFV8TjxsO-XushNB958wK-7YdGziwDlKRK_Mg.9woWfG2L7SkVjD5uCZNNfXMJaeV6WnEUTIjPXwJkzbwg.PNG.galaxyenergy/20170906_203003.png?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMjk3/MDAxNTA0Njk3NDc2MjUy.OIiWJaUAsLVkOmz6q2_qv3INP5_cvxRRGgS45Xkb_64g.1btrhXgI-IirugqH5t3u0vLLTQ-EnhOv9hXbmaXSkyYg.JPEG.galaxyenergy/1504697104328.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) *일반항이건 합이건* *공식이 있어* *공식에 숫자만 집어넣으면 답이 나온다* *등비수열의 합을* *공식을 모른다 치고 구해 보자* [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMzQg/MDAxNTA0Njk3NTA2MDE2.qY75dq7Om7ervf1dbenNVvlzP5oD058NP_diaOQJMeQg.bXVf1XP855o5fq4Y5dAVScvjpVDDuMAiBvhiJVGMjVYg.JPEG.galaxyenergy/5-018-140rei.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMTcg/MDAxNTA0Njk3NTM4NTMw.j-grs2E7XnufEyqh3JJT9UNX6DxawnYZ2hKZ-Y_UGqsg.r_mqJxD1Sc3GFKARhm0n9GfNCpjesWqv88KOJuV-kKQg.JPEG.galaxyenergy/20170906_194633.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) *다음과 같은* *101 개의 숫자들을* *몽땅 합치면* *그 합은 얼마냐 ?* *이것을 등비수열의 합이라고 한다* [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMjI3/MDAxNTA0NzA5MTkzNzE4.hi83DzhZvf4inaai4lXvBuofVTCVjaTI8jZu9Ule17Yg.ufAMfD642Zh8zjDX7F9UZ68RN4YKRFkQQ-zEuMMi_Jcg.JPEG.galaxyenergy/20170906_194720.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) *자세히 보면* *개수는 모두 101 개다* *이 101 개라는 개수를* *항수 혹은 n 이라고 한다* [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfNzMg/MDAxNTA0Njk3NjI2NDEw.VKzLCnQRGyAFZzPzciwL_59Q75lOvE_VSHdVK-2Li5wg.pNWujrQ_Zqxl6DtO5c5Uf2WTHb9-ELPXL_OQc8qDuM4g.JPEG.galaxyenergy/20170906_194655.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) *이 숫자들이 늘어선 규칙은* *(항상 앞의 것에 ×2 하면 뒤의 것이다)* *2를* *공비 혹은 r 이라고 한다* [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMTk3/MDAxNTA0Njk3NjYzMDM0.40Fj14UhgnPekdXhnG2VxU16cnDxs_-buq7s8t0u5oQg.1ZDu-dvYC_yl28WfZgQqodq9v0NH96_8AXqpq79lEhgg.JPEG.galaxyenergy/17-09-06-19-43-47-562_deco.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) *그리고* *맨 앞에 있는 저것을* *초항 혹은 a라고 한다* *(여기서는 1을 가리킨다)* [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMTcw/MDAxNTA0Njk3Njg1MzA3.FtlHjasDyVQ1r47_oU3C5LXMm6lYsMk48vpb2bkAPbAg.JJ1fhrhLD8in9EK7bkm6ak-SjXKYjXujX1WG87UILf8g.JPEG.galaxyenergy/1504697104328.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) *저 101 개의 숫자들의 합을 구하는* *공식이 있는데* *공식을 모른다 가정하고 구해보자* [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMjkx/MDAxNTA0Njk3NzAwNDc3.Uaxrv2HDzBFbd9B81B-9r_5wA5gfOdxhdfF5XJtFcy8g.HgiTsVkPJo-9VHZRABRfBm5YlGH6TDyBihHuRCSkNK0g.JPEG.galaxyenergy/20170906_194633.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) *일단* *몽땅 합친 것을 S라고 하자* *(S를 구하는 것이 목적이다)* *저 101 개의 숫자들을* *하나하나 합쳐서 전체 합을 구하는 것은* *미친 짓이다* *수학적 테크닉과 기교를 사용해야 한다* [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMjAz/MDAxNTA0Njk3ODAyMTgx.SgKw2X3LN7LTEpY0Vi55rroNOeLYP6QrICbn-NUj88Ug.j4ogjhx1tNA1ltGLZrtBuet-MByiy2UmOELL3ZVwg_4g.JPEG.galaxyenergy/1504697782868.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) *S에* *공비 2를 곱해서* *2S라는 새로운 식을 만든다* [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMTc5/MDAxNTA0Njk3ODMwODgy.qEElsoVSR5644gnhqy1o3HhtSbHlCWP3cELjpxKA8GMg.UkSPEDWMgcG6r8ZQDPo85Hmfa1XYIibA-DlQRKKdhcgg.JPEG.galaxyenergy/1504697829750.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) *그 다음* *2S에서 S를 빼준다* *그러면 빼주는 과정에서* *같은 것끼리는 다 지워지고* *딱 두 개만 남는다* [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMjE4/MDAxNTA0Njk3ODg2NjYz.uoWUhIqKFovNW_pAFsXLlNct0V__HjIHO-2zdggFDuUg.EVPoOlWJD9vq5S0vEqyfo-pPkH2sTttgTZ6PE9HuDCMg.JPEG.galaxyenergy/1504697883943.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) *그것이 답이다* [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMTI1/MDAxNTA0Njk3OTA4MjE3.NaL6e7BEpinPm62xjbCmtthElfZlr0VgjS_0Y7djNngg.dzHXWKvYM24-In68FK6prQiaFa_ezehiqpt1g8HroOYg.PNG.galaxyenergy/3-1.png?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) *사실은 이것이* *등비수열의 합공식을 만드는* *과정이기도 하다* [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMjMz/MDAxNTA0Njk3OTI0OTY0.zjhd3N4pZ7BIT7ZdZm0L-vtrFxKNMtL3-UvaYC5Zkn0g.FgS2IFaQZxMrqSY0wq5NP2CwgSO4CVAHnvISEfvyz0Yg.PNG.galaxyenergy/20170906_201840.png?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMjQw/MDAxNTA0Njk4MDEwNTMx.seAVCI42SFXCghwK1oitQZThURWw_571hHBngwDNvmkg.qTr2n4J9gEins4jAH7SAPP8_rwYi_HpZnLupfiDHb6Yg.PNG.galaxyenergy/20170828_161457.png?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://dthumb-phinf.pstatic.net/?src=%22https%3A%2F%2Fblogthumb.pstatic.net%2FMjAxOTA2MTFfNzYg%2FMDAxNTYwMjM3MjY0NzEy.DVBcX4On0B0qxPtP-tri4OmixKC5bmNgx3Afw5-O18gg.L3eBJo-rPiESh-wvZYIx0A1yrFIFeJ2MCWTalN3E8sIg.JPEG.galaxyenergy%2F1546514456981.jpg%3Ftype%3Dw2%22&type=ff500_300) 미분 도함수 기하와 도형으로 이해하기 미분을 기하와 도형으로 이해해야 진정으로 미분을 이해한다고 할 수 있다 x²을 미분하면 2x 이런 식으로 ... m.blog.naver.com](https://m.blog.naver.com/galaxyenergy/221559554463) [![](https://dthumb-phinf.pstatic.net/?src=%22https%3A%2F%2Fblogthumb.pstatic.net%2FMjAxOTA0MTFfMTgz%2FMDAxNTU0OTY0MjUzMjg1.eFC1trq-nmcJdkAWFO4X-nsvwb2t_k86KeJQ2sHfmRsg.pLTh6LwGKI_OrpG8XRTd1zgI-fAznYVvWK35xarMycIg.JPEG.galaxyenergy%2FBandPhoto_3169198329.jpg%3Ftype%3Dw2%22&type=ff500_300) 합성함수 미분 기하와 산수로 이해하기 합성함수 미분은 미적분의 최대의 키포인트다 (치환적분도 합성함수 미분의 역이다) y = (x³+ 5x²)⁴+ 6(x³... m.blog.naver.com](https://m.blog.naver.com/galaxyenergy/221511145415) [![](https://dthumb-phinf.pstatic.net/?src=%22https%3A%2F%2Fblogthumb.pstatic.net%2FMjAxODExMzBfMjE2%2FMDAxNTQzNTc5MjEzMjU0.uU2cx8NfRTT7vPhIo6t3R_sfuVgLuAgCe-8SzTsSdXUg.BviFktwtlqH-eI9rpjXWJYMBKfT546NZHXvRgNZMVswg.JPEG.galaxyenergy%2FBandPhoto_3169198329.jpg%3Ftype%3Dw2%22&type=ff500_300) 합성함수 미분 연애와 키스 원리로 이해하기 합성함수 미분이란 함수의 한 점에서의 기울기를 (미분) 구하기 어려우니까 두 개의 기울기를 곱하는 방법... m.blog.naver.com](https://m.blog.naver.com/galaxyenergy/221409757973) [![](https://dthumb-phinf.pstatic.net/?src=%22https%3A%2F%2Fblogthumb.pstatic.net%2FMjAxODExMjlfMjQw%2FMDAxNTQzNDkwNDQ0MDcz.PjXbQwEFoeeV45-mItW10wL3G6nk0dHS2pPJdibrkMIg.AXsFgYVRrqjPbf4OcbKJdX_lWg4YJYf3JrlC1JVm-60g.JPEG.galaxyenergy%2F1537009857598.jpg%3Ftype%3Dw2%22&type=ff120) 치환적분 기하와 도형으로 이해하기 치환적분 말뜻을 알고 고등학교 졸업한 사람은 100명 중 1명도 안 되고 대학교에서도 계속 두드려외운다 3x... m.blog.naver.com](https://m.blog.naver.com/galaxyenergy/221408975283) [![](https://dthumb-phinf.pstatic.net/?src=%22https%3A%2F%2Fblogthumb.pstatic.net%2FMjAxODA2MjhfMyAg%2FMDAxNTMwMTg2MzMxMjQw.zMB6B__ixnS3opUM8um8dIXvIs02s8pdX9zhSF4rRF4g.xyuQQ1wbtTB30v7Wq7Rt-6bilAV9BWq-FoDzdl61hK8g.JPEG.galaxyenergy%2F1530184165865.jpg%3Ftype%3Dw2%22&type=ff500_300) 삼각비 삼각함수 일반각 단위원 종합적으로 이해하기 중학교 때는 (0 ° \~~ 90°) 범위의 삼각함수만 다룬다 (그냥 삼각비라 부른다) 고등학교 때는 구간이 ( -∞ ... m.blog.naver.com](https://m.blog.naver.com/galaxyenergy/221308833389) [![](https://dthumb-phinf.pstatic.net/?src=%22https%3A%2F%2Fblogthumb.pstatic.net%2FMjAxODAyMDJfMjAw%2FMDAxNTE3NTcyNjEwODM3.D9v3TJ-Azd84gm2aWpCSz1OqE8y5rPzGX3FT8csFmiog.fjSeHdqGZI9z0_ohwuaYZFkPqftH8PfgycWF6k2Uf_Qg.JPEG.galaxyenergy%2FBandPhoto_3169198329.jpg%3Ftype%3Dw2%22&type=ff500_300) 일반각 삼각함수 난해한 어려운 세계 가볍게 정복하기 정말 어려운 것이라서 고등학교 때는 그냥 무조건 외우고 무조건 외우는 그것조차 너무나 힘이 들어서 수학... m.blog.naver.com](https://m.blog.naver.com/galaxyenergy/221199814872) [![](https://mblogthumb-phinf.pstatic.net/MjAxODA5MTlfMjU3/MDAxNTM3MzQ3NDA0NTcy.HMul9zL_lYipunM6LVqJe0gn_bN63UiLZJDXa-v3-UAg.2BDYkJb9EhnVDUv2QmQzu4uuBRP7xbAxNdQ2_BhGm3Yg.JPEG.galaxyenergy/1536734308740.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxODA2MjJfMjEw/MDAxNTI5NjUwOTcwNTk4.JJwcAItanZXYHIw4aZDwuh0OdY3hbE99iSU5Y1_rs94g.Xo0UQw5s0KMpbVrOeTRcr9UqNzv0AZ-P3fZaSWRX-6Mg.JPEG.galaxyenergy/1529475454325.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxODA5MTlfMTk4/MDAxNTM3MzQ3NDA3MTgx.HABDGcpIQQgwGQEtw0_ZPcLZONpY7O9h0qLsS_B8Vd4g._u_axrjLfS7tf99me0281LDT73HAUuKYJuFh5quCtHwg.JPEG.galaxyenergy/1527423288997.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxODA5MTlfMTM1/MDAxNTM3MzQ3NDA4MTM5.alNrghghhtuCgMvybTqUVTMdK-4VvJwmfWhrCIWTIvgg.U6v4Emk_YenSVqKMxaoVvS0qDyloTAdBPqvW56qMODYg.JPEG.galaxyenergy/1535108819189.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxODA5MTlfOTMg/MDAxNTM3MzQ3NDA5MDYy.8b8bNc92s328ACEGyikjy0MzG5vm9ODQDDMxAt80WREg.v7ePdbIUYu8gWsdlDWNYK_OfuF4_athQo-xzV2o-QKMg.JPEG.galaxyenergy/1535109183971.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxODA2MjJfMTMw/MDAxNTI5NjUwOTcxNDY4.0a1ywrSvPwiFc_FQWqmdaV-Y72f7S_yLmoYo6lhl7dEg.NxqlOIvgdOfxCMsPIMsnPZacsUmyr9b1RbHAW6a1mEAg.JPEG.galaxyenergy/1529475606443.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxODA2MjJfMTM1/MDAxNTI5NjUwOTcyNDI2.CDR6UgEE16I8W2ylYDYzYIVjnLhCFN0DKjGMmPjG3mwg.IxYK97XepC6Thdg7X4a113a5SSWkZ2dHmdQdtwI2yJ4g.JPEG.galaxyenergy/1529475629680.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxODA2MjJfMTk4/MDAxNTI5NjUwOTc0MzE4.VWjPJWjas0tSkNbuk3q1z-gaYkRbLsHMilBVHK1pdw4g.mtMc_9yrG6Xcsy2_CXbhuxy2e0vl7PrY1Rs_FGeEtrgg.JPEG.galaxyenergy/1529475800484.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxODA2MjJfNTgg/MDAxNTI5NjUwOTc1MzQz.RIYVNR97psA2l2nokiPA5lo0gF6Uko3CbbjdoH7IVKUg.rYDqX4rTCZcRfv1psbSyK6yPkIj3QU_eR_FACOFtP0gg.JPEG.galaxyenergy/1526557599463.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxODA2MjJfMjM2/MDAxNTI5NjUwOTc2NDE5.0X7H-EOzsq-S5gEZ1xTIapANdGSS9RjDxsO3K_461EAg.wIrxwLfjA9he2je4PQID_XjbYWsmKPeyO1ozmfuM8aIg.JPEG.galaxyenergy/1526556614549.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxODA2MjJfMTA3/MDAxNTI5NjUwOTc3Mjcy.tM7pz2QiXadA_YNB7XIh0XTFI7FjMIsBZrvGYRXM-H4g.45eiGiHUbiIX0Uo1pffvsK2sv4qfoDOVTcNCaW_STzQg.JPEG.galaxyenergy/1529405155340.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxODA2MjJfMTU0/MDAxNTI5NjUwOTc4MjA1.pvHov-A_idjF9IlTfIVABI4-zUeMh26bg7wqDK4hXP8g.ePM2r_DYRN1e7KESf6e0Gw9oupP6iUUpzDmYXjGEyhkg.JPEG.galaxyenergy/1529405042781.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfNDMg/MDAxNTA0Njk4MDQxMTk1.qtw5VKrex2S2Wm2odpueH6BPWPknXE4mQ_xExpTv-Asg.bcLp7LkqvNwIpJZmNIPKoSFpOSRk2v5n6EKSu_XuXvAg.JPEG.galaxyenergy/mugc-1.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMTM1/MDAxNTA0Njk4MDQxNTgz.p3wXyXiuPciRoaZYI328sCkkfeAJVioJr_sR4Zxfzc4g.jGi4KIssrpaDvLxO5rCjv0jLa6IorL24pYyad1ci2Pog.PNG.galaxyenergy/%EB%8B%B9%ED%99%A9_%EB%A8%B8%ED%81%90%EB%A6%AC.png?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfOTYg/MDAxNTA0Njk4MDQxODkx.Jd2auNpPW7a1lgU6uzZhAdSJEfGpwxeFD_qaI4BKYwMg.3mVHL26aRStMVUeL73Q_LaNR46exa4oCMgMQThYsaaYg.PNG.galaxyenergy/Screenshot_2015-08-11-18-03-42-1.png?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMjU2/MDAxNTA0Njk4MDQyMTgy.BTypn3l1YtKrujDd13f3vsuguyQes3AbYWlE37W1klcg.16q3ZaC02UTnqOaplDmKrOBnC_5c0Lwt42sY3lCkXFcg.JPEG.galaxyenergy/BandPhoto_3169198329.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMTYx/MDAxNTA0Njk4MTcwMTMy.AD7MutvXzgrcKbXiWmXU2uAnUBGt4MIC0oOnsPNSnT0g.P0wIphKerd8GEndcE0Lt-eDO36sR9a2Evb-6eTeD6Vcg.JPEG.galaxyenergy/mugc-123.jpeg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMjU2/MDAxNTA0Njk4MTcxMDIx.mtSBif-ijrYrBTkrhovIA7cRCa3XllteGTH-8Z3ANEog.zmVgH5WiBPFw-SFlqeNw4W55B2y2KVZTnLFjXCsT6DYg.JPEG.galaxyenergy/0125kiss.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfNSAg/MDAxNTA0Njk4MTcxNjc3.s3H7vl4QOHX48mfsESFBMX0tyAWc7aTKiePttZ710FYg.1oGs1MecGaNY5DfL1IlNW13DiF4ieqGZaCAxwhxqsv8g.JPEG.galaxyenergy/7201280.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfOTUg/MDAxNTA0Njk4MTcyNjQy.3lxcHgeHP9SDZ4VAqvTKsDsSBnS8ukI1ugi0OPnvFxwg.el1I1e6R1ccwn5jmpHykLLlNCjCZA0s8_irHf5AlE9Mg.JPEG.galaxyenergy/an_w_copy.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfOCAg/MDAxNTA0Njk4MTc0NDgz.sznzrptrevf-RuGZBRQTTLJvd0zkhOvEVuavgwI0jkMg.GfrPh24SZLoR7UHg307CpnFgaN9UtxmivmUazK1ddIEg.JPEG.galaxyenergy/mugc-52.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMjU4/MDAxNTA0Njk4MTc1MDg0.UhASiFHqD_s31YaJ29oQHdNGwZs8pLTo-fbrKmiSsQcg.yeByjlWP6yJ6dPcQUn_P4KHWet5eqkdYEk_iS-u0wOAg.JPEG.galaxyenergy/mugc-54.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMjQ1/MDAxNTA0Njk4MTc2MTg2.7fTABkBy3t-kFHDfkiTDfo3XPmFPQYJ5ih5fbLZCq00g.j0F8Let_5ijizWoZeQ7OP23RkkDlz6NX1_Kg63POAPgg.JPEG.galaxyenergy/mugc-43.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMTM1/MDAxNTA0Njk4MTc2OTQw.6H0tPk4cANpXpIZ29W73nqr-pwvxKSoybiRitSsEIsEg.B7yROXP_Cd89Ibl2HnynDCHxizHMnomAfMQ4Y_VXKTYg.JPEG.galaxyenergy/mugc-41.jpeg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMjEg/MDAxNTA0Njk4MTM0ODI1.K-0JNqmylIyEixX8dQzrh3NCUqsN2AcLGEVxUFHYs-4g.lZF6UJSjY4IjSGuP-3pGra4eijXFxtl4rQJW3XC1scMg.JPEG.galaxyenergy/1504698133118.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMjkx/MDAxNTA0Njk4MjUxMjYx._sZtdPlEa_QxRMxo9H_lth2hlRIZPXbRNcs2thTHKkkg.TWVBflqAb3v_77lmmWX74UClWf7PhGIYj2pUuyywDtUg.JPEG.galaxyenergy/17-08-14-19-45-44-829_deco.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMjAw/MDAxNTA0Njk4MjUyNzEx.PTuzyJUXalAq5Xn0SHC7mRybQOf68zlqU7iWqQJWbpcg.IoyrqN0GqXmZFGnEAZ9L8VGQiHPyp6XZZAnVSwEMyu0g.JPEG.galaxyenergy/17-08-14-19-44-55-921_deco.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMjc5/MDAxNTA0Njk4MjUzNDg3.krAVcXPCqaiUIgDGU0e2s86CHD2f0LAUzeL6MyT88r4g.HmRxahNDOxUbgfouDLknhysvHLki6kUhtAIe7A-M7cIg.JPEG.galaxyenergy/17-08-14-19-43-33-955_deco.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) [![](https://mblogthumb-phinf.pstatic.net/MjAxNzA5MDZfMjU2/MDAxNTA0Njk4MjU0NDQy.PBtKwf4o5v2gj3Qx0ByGgCSJVAgdihNzYWlc082aM5cg.9FMDJlq5v0JikXf2vT04MIY-j8cSJNxGpVXIvSM5l_Yg.JPEG.galaxyenergy/17-08-14-19-46-46-238_deco.jpg?type=w80_blur)](https://m.blog.naver.com/galaxyenergy/221090965396) 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