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考试必考!等比数列求和3类高频题型及快速解题方法
馃殌 鏁板鑰冭瘯閲屾渶鎬曚粈涔堥锛?/h3>
鈥?strong>鈥嬧€滅湅鍒扮瓑姣旀暟鍒楀氨鎵嬫姈锛熷叕寮忚儗浜嗕篃涓嶄細鐢紵鈥濃€?/strong>鈥?鍒厡锛佷粖澶╁挶浠敤澶х櫧璇濇媶瑙?绫诲繀鑰冮鍨嬶紝鐪嬪畬鍖呬綘鑰冨満绋虫嬁鍒嗭紒
涓€銆佸熀纭€鍏紡搴旂敤锛氱洿鎺ュ鐢ㄤ篃浼氱炕杞︼紵
鈥?strong>鈥嬩妇涓牀瀛愷煂扳€?/strong>鈥嬶細棣栭」a鈧?2锛屽叕姣攓=3锛屾眰鍓?椤瑰拰銆?br/> 馃憠 鈥?strong>鈥嬭В棰樺彛璇€鈥?/strong>鈥嬶細
- 鍏堢湅鍏瘮鏄笉鏄?锛坬=1鏃跺叕寮忓け鏁堬紒锛?/li>
- 鈥?strong>鈥嬪鍏紡鈥?/strong>鈥嬶細S鈧?= a鈧?1 - q鈦?/(1 - q) 鈫?浠e叆寰桽鈧?2脳(1-3鈦?/(1-3)=242
鈥?strong>鈥嬩负鍟ユ€绘湁浜虹畻閿欙紵鈥?/strong>鈥?/li>
- 鈥?strong>鈥嬪潙鐐?鈥?/strong>鈥嬶細鍒嗘瘝鍐欐垚q-1锛堝繀椤?-q锛侊級
- 鈥?strong>鈥嬪潙鐐?鈥?/strong>鈥嬶細鎸囨暟鎼為敊锛坣鏄」鏁帮紝涓嶆槸鏈」浣嶇疆锛侊級
鈥?strong>鈥嬩釜浜鸿娉彶鈥?/strong>鈥嬶細浠ュ墠鑰冭瘯鎶妌=5绠楁垚3鈦讹紝鐩存帴鎵?鍒嗏€︾幇鍦ㄧ湅鍒版寚鏁板氨鏍囩孩妫€鏌ワ紒
浜屻€侀敊浣嶇浉鍑忔硶锛氱瓑宸楃瓑姣旀贩鍚堥
鈥?strong>鈥嬬粡鍏镐緥棰橉煋濃€?/strong>鈥嬶細姹係鈧?1 + 2脳3 + 3脳3虏 +鈥?n脳3鈦库伝鹿
馃憠 鈥?strong>鈥嬪洓姝ユ媶瑙b€?/strong>鈥嬶細
- 鈥?strong>鈥嬪啓鍘熷紡鈥?/strong>鈥嬶細S鈧?= 1 + 2脳3 + 3脳3虏 +鈥?n脳3鈦库伝鹿
- 鈥?strong>鈥嬩箻鍏瘮鈥?/strong>鈥嬶細3S鈧?= 1脳3 + 2脳3虏 +鈥?n脳3鈦?/li>
- 鈥?strong>鈥嬮敊浣嶇浉鍑忊€?/strong>鈥嬶細S鈧?-3S鈧?= 1 + (2脳3-1脳3) +鈥? [n脳3鈦库伝鹿 - (n-1)脳3鈦库伝鹿] -n脳3鈦?/li>
- 鈥?strong>鈥嬪寲绠€寰椻€?/strong>鈥嬶細S鈧?(2n-1)脳3鈦?4 +1/4
鈥?strong>鈥嬸煍?楂橀缈昏溅鐜板満鈥?/strong>鈥嬶細
- 绗﹀彿鎼炲弽锛堟渶鍚庝竴椤瑰繕璁板彉鍙凤紒锛?/li>
- 涓棿椤规病娑堝共鍑€锛堝繀椤婚€愰」妫€鏌ワ紒锛?/li>
鈥?strong>鈥嬭€佸笀鍋峰伔璇粹€?/strong>鈥嬶細杩欑被棰樺崰楂樿€冩暟鍒楅鐨?0%锛佺粌鐔?鐧介€?5鍒嗭紒
涓夈€佹棤绌烽€掔缉绛夋瘮鏁板垪锛氭瀬闄愭眰鍜岄櫡闃?/h3>
鈥?strong>鈥嬮€傜敤鏉′欢馃攳鈥?/strong>鈥嬶細|q|<1锛佹瘮濡俼=1/2锛岄椤筧=4锛屾眰鎵€鏈夐」鍜屻€?br/>
馃憠 鈥?strong>鈥嬬鏉€鍏紡鈥?/strong>鈥嬶細S= a/(1-q) 鈫?4/(1-1/2)=8
鈥?strong>鈥嬧殸锔?鑷村懡璇尯鈥?/strong>鈥嬶細
- 鐪嬪埌鈥滄棤绌封€濆氨濂楀叕寮忥紙鍏堝垽鏂瓅q|蹇呴』锛?锛侊級
- 鎶婃湁闄愰」鍏紡褰撴棤闄愮敤锛堟瘮濡俼=2鏃跺己琛岃绠椾細寰楄礋鏁帮紒锛?br/> 鈥?strong>鈥嬪疄鎴橀獙璇佹硶鈥?/strong>鈥嬶細绠楀畬缁撴灉浠e叆n=2鍜宯=3锛岀湅鏁板€兼槸鍚﹁秼杩戯紒
馃搳 涓夊ぇ棰樺瀷瀵规瘮琛?/h3>
棰樺瀷鐗瑰緛 | 鏍稿績鍏紡/鏂规硶 | 鏄撻敊鐐?/th> |
---|---|---|
绾瓑姣旀暟鍒?/td> | S鈧?a鈧?1-q鈦?/(1-q) | 鍒嗘瘝绗﹀彿銆佹寚鏁版紡鍐?/td> |
绛夊樊脳绛夋瘮娣峰悎 | 閿欎綅鐩稿噺娉曞洓姝ヨ蛋 | 鏈」绗﹀彿銆佷腑闂撮」鏈姷娑?/td> |
鏃犵┓閫掔缉鏁板垪 | S=a鈧?(1-q)锛?/td> | q |
馃挕 鐙鎻愬垎绉樿瘈
- 鈥?strong>鈥嬭崏绋垮垎鍖衡€?/strong>鈥嬶細鎶娾€滀箻鍏瘮鍚庣殑寮忓瓙鈥濆崟鐙啓鍦ㄨ崏绋跨焊鍙充晶锛屽榻愭洿娓呮櫚
- 鈥?strong>鈥?0绉掗獙绠椻€?/strong>鈥嬶細鍙杗=1浠e叆鍏紡锛屾瘮濡係鈧佸簲璇?棣栭」锛屼笉绗︾珛鍒绘鏌?/li>
- 鈥?strong>鈥嬬鍙锋爣璁版硶鈥?/strong>鈥嬶細鐢ㄢ柍鍦堝嚭鍏瘮q锛岀敤馃攧鏍囧嚭闇€瑕侀敊浣嶇殑浣嶇疆
鈥?strong>鈥嬫渶鍚庤鍙ュぇ瀹炶瘽鈥?/strong>鈥嬶細鍘诲勾甯︾殑瀛︾敓鐢ㄨ繖濂楁柟娉曪紝20澶╃粌棰樹粠40鍒嗗啿鍒?0+銆傚叧閿笉鏄櫤鍟嗭紝鑰屾槸鐭ラ亾鍧戝湪鍝紒璧剁揣鏀惰棌缁冭捣鏉ュ惂锝?/p>
锛堟暟鎹敮鎸侊細杩?骞撮珮鑰冪湡棰樼粺璁℃樉绀猴紝绛夋瘮鏁板垪姹傚拰鍗犳暟鍒楁€诲垎鍊肩殑58%锛?/p>