(完整word版)高中数学数列知识点总结(经典)(2),推荐文档.pdf

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1、高一数学期末复习专题解三角形1正弦定理:2sinsinsinabcRABC:sin:sin:sina b cABC.2余弦定理：2222222222cos2cos2cosabcbcAbacacBcbabaC或222222222cos2cos2cos2bcaAbcacbBacbacCab.3正、余玄定理的解题类型：（1）两类正弦定理解三角形的问题：已知两角和任意一边，求其他的两边及一角.已知两角和其中一边的对角，求其他边角.（2）两类余弦定理解三角形的问题：已知三边求三角.已知两边和他们的夹角，求第三边和其他两角.4判定三角形形状时，可利用正余弦定理实现边角转化，统一成边的形式或角的形式.5解题

2、中利用ABC中：ABC，以及由此推得的一些基本关系式进行三角变换的运算，如：sin()sin,ABC cos()cos,ABCtan()tan,ABCsincos,cossin,tancot222222ABCABCABC.6、三角公式：（1）倍角公式：（2）两角和、差公式：1 数列基础知识点和方法归纳1.等差数列的定义与性质（1）定义：1nnaad（d 为常数），通项公式：11naand（2）等差中项：xAy，成等差数列2Axy（3）前 n项和：11122nnaann nSnad（4）性质：na是等差数列任意两项间的关系式；anam(nm)d（m、nN）若 mnpq，则mnpqaaaa；232

3、nnnnnSSSSS，仍为等差数列，公差为dn2；若三个成等差数列，可设为adaad，若nnab，是等差数列，且前 n项和分别为nnST，则2121mmmmaSbTna为等差数列2nSanbn（ab，为常数，是关于 n的常数项为 0 的二次函数）nS的最值可求二次函数2nSanbn的最值；或者求出na中的正、负分界项，即：当100ad，解不等式组100nnaa可得nS达到最大值时的 n值.当100ad，由100nnaa可得nS达到最小值时的 n值.项数为偶数n2 的等差数列na，有),)()()(11122212为中间两项nnnnnnnaaaanaanaanSndSS奇偶，1nnaaSS偶奇.

4、项数为奇数12n的等差数列na，有：)()12(12为中间项nnnaanS，naSS偶奇，1nnSS偶奇.2 文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:

5、CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I

6、4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:

7、CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I

8、4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:

9、CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I

10、4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A62.等比数列的定义与性质（1）定义：1nnaqa（q 为常数，0q），通项公式：11nnaaq.（2）等比中项：xGy、成等比数列2Gxy，或 Gxy.（3）前 n项和：11(1)1(1)1nnna qSaqqq（要注意！）（4）性质：na是等比数列

11、任意两项间的关系：aman.qmn（m、nN）.若 mnpq，则mnpqaaaa232nnnnnSSSSS，仍为等比数列，公比为nq.注意：由nS求na时应注意什么？1n时，11aS；2n时，1nnnaSS.3求数列通项公式的常用方法（1）求差（商）法如：数列na，12211125222nnaaan，求na解：1n时，112 152a，114a2n时，12121111215222nnaaan得：122nna，12nna，114(1)2(2)nnnan练习数列na满足111543nnnSSaa，求na注意到11nnnaSS，代入得14nnSS；又14S，nS是等比数列，4nnS2n时，113 4

12、nnnnaSS文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P

13、5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X

14、4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P

15、5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X

16、4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P

17、5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X

18、4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6（2）叠乘法如：数列na中，1131nnanaan，求na解：321211 212 3nnaaanaaan，11naan又13a，3nan.（3）等差型递推公式由110()nnaaf naa，求na，用迭加法2n时，21321(2)(3)()nnaafaafaaf n 两边相加得1(2)(3)()naafff n0(2)(3)()naafff

19、n练习数列na中，111132nnnaaan，求na（1312nna）（4）等比型递推公式1nnacad（cd、为常数，010ccd，）可转化为等比数列，设111nnnnaxc axacacx令(1)cxd，1dxc，1ndac是首项为11dacc，为公比的等比数列1111nnddaaccc，1111nnddaaccc（5）倒数法如：11212nnnaaaa，求na由已知得：1211122nnnnaaaa，11112nnaa1na为等差数列，111a，公差为12，11111122nnna，21nan(附：公 式 法、利 用1(2)1(1)nnSSnS nna、累 加 法、累 乘 法.构 造 等

20、 差 或 等 比1nnapaq或1()nnapaf n、待定系数法、对数变换法、迭代法、数学归纳法、文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1

21、X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 Z

22、A5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1

23、X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 Z

24、A5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1

25、X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 Z

26、A5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6换元法)4.求数列前 n 项和的常用方法（1）公式法（2）裂项相消法把数列各项拆成两项或多项之和，使之出现成对互为相反数的项.如：na是公差为 d 的等差数列，求111nkkka a解：由11111110kkkkkkdaaaaddaa1111122311111

27、1111111nnkkkkkknna adaadaaaaaa11111ndaa练习求和：111112123123n121nnaSn，（3）错位相减法若na为等差数列，nb为等比数列，求数列nna b（差比数列）前 n项和，可由nnSqS，求nS，其中 q为nb的公比.如：2311234nnSxxxnx23412341nnnx Sxxxxnxnx2111nnnx Sxxxnx1x时，2111nnnxnxSxx，1x时，11232nn nSn（4）分组求和法所谓分组求和法就是对一类既不是等差数列，也不是等比数列的数列，若将这类数列适当拆开，可分为几个等差、等比或常见的数列，然后分别求和，再将其合并

28、。（5）倒序相加法把数列的各项顺序倒写，再与原来顺序的数列相加.文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9 ZA5X4F7R9A6文档编码:CO8S1X5P5T4 HW1Q9E2I4T9

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