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2022年数列解题技巧归纳总结-打印3 .pdf

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1、。-可编辑修改-等差数列前n项和的最值问题：1、若等差数列na的首项10a，公差0d，则前n项和nS有最大值。（）若已知通项na，则nS最大100nnaa；（）若已知2nSpnqn，则当n取最靠近2qp的非零自然数时nS最大；2、若等差数列na的首项10a，公差0d，则前n项和nS有最小值（）若已知通项na，则nS最小100nnaa；（）若已知2nSpnqn，则当n取最靠近2qp的非零自然数时nS最小；数列通项的求法：公式法：等差数列通项公式；等比数列通项公式。已知nS（即12()naaaf n）求na，用作差法：11,(1),(2)nnnSnaSSn。已知12()na aaf n求na，用作

2、商法：(1),(1)(),(2)(1)nfnf nanf n。已知条件中既有nS还有na，有时先求nS，再求na；有时也可直接求na。若1()nnaaf n求na用累加法：11221()()()nnnnnaaaaaaa1a(2)n。已知1()nnaf na求na，用累乘法：121121nnnnnaaaaaaaa(2)n。已知递推关系求na，用构造法（构造等差、等比数列）。特别地，（1）形如1nnakab、1nnnakab（,k b为常数）的递推数列都可以用待定系数法转化为公比为k的等比数列后，再求na；形如1nnnakak的递推数列都可以除以nk得到一个等差数列后，再求na。（2）形如11n

3、nnaakab的递推数列都可以用倒数法求通项。（3）形如1knnaa的递推数列都可以用对数法求通项。（7）（理科）数学归纳法。-可编辑修改-（8）当遇到qaadaannnn1111或时，分奇数项偶数项讨论，结果可能是分段一、典型题的技巧解法1、求通项公式（1）观察法。（2）由递推公式求通项。对于由递推公式所确定的数列的求解，通常可通过对递推公式的变换转化成等差数列或等比数列问题。(1)递推式为 an+1=an+d 及 an+1=qan（d，q 为常数）例 1、已知 an 满足 an+1=an+2，而且 a1=1。求 an。例 1、解an+1-an=2 为常数an是首项为1，公差为2 的等差数列

4、an=1+2（n-1）即 an=2n-1 例 2、已知na满足112nnaa，而12a，求na=？（2）递推式为 an+1=an+f（n）例 3、已知na中112a，12141nnaan，求na.解：由已知可知)12)(12(11nnaann)121121(21nn令 n=1，2，（n-1），代入得（n-1）个等式累加，即（a2-a1）+（a3-a2）+（an-an-1）2434)1211(211nnnaan说明只要和f（1）+f（2）+f（n-1）是可求的，就可以由an+1=an+f（n）以 n=1，2，（n-1）代入，可得n-1 个等式累加而求an。(3)递推式为 an+1=pan+q（p

5、，q 为常数）例 4、na中，11a，对于 n1（n N）有132nnaa，求na.解法一：由已知递推式得an+1=3an+2，an=3an-1+2。两式相减：an+1-an=3（an-an-1）因此数列 an+1-an是公比为3 的等比数列，其首项为a2-a1=（3 1+2）-1=4 an+1-an=43n-1an+1=3an+23an+2-an=43n-1 即 an=23n-1-1 解法二：上法得 an+1-an是公比为3 的等比数列，于是有：a2-a1=4，a3-a2=4 3，a4-a3=4 32，an-an-1=4 3n-2，把 n-1 个等式累加得：an=23n-1-1 文档编码:C

6、U4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6

7、A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:C

8、U4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6

9、A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:C

10、U4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6

11、A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:C

12、U4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7文档编码:CU4T5A5Z7X4 HD7W1H5H6A5 ZI5A2H3V4Z7。-可编辑修改-(4)递推式为 an+1=p an+q n（p，q 为常数）)(3211nnnnbbbb由上题的解法，得：nnb)32(23nnnnnba)31(2)21(32(5)递推式为21nnnapaqa思路：设21nnnapaqa,可以变形为：211()nnnnaaaa，想于是 an+1-an是公比为的等比数列，就转化为前面的类型。求na。(6)递推式为 Sn与

13、 an的关系式文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P

14、8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T

15、1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P

16、8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T

17、1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P

18、8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T

19、1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3。-可编辑修改-关系；（2）试用 n表示 an。)2121()(1211nnnnnnaaSS11121nnnnaaannnaa21211上式两边同乘以2n+1得 2n+1an+1=2nan+2 则2nan 是公差为 2 的等差数列。2nan=2+（n-1）2=2n 2数列求和问题的方法（1）、应用公式法等差、等比数列可直接利用等差、等比数列的前

20、n项和公式求和，另外记住以下公式对求和来说是有益的。13 5(2n-1)=n2【例 8】求数列 1，（3+5），（7+9+10），（13+15+17+19），前 n 项的和。解本题实际是求各奇数的和，在数列的前n 项中，共有1+2+n=)1(21nn个奇数，最后一个奇数为：1+21n(n+1)-12=n2+n-1 因此所求数列的前n 项的和为（2）、分解转化法对通项进行分解、组合,转化为等差数列或等比数列求和。【例 9】求和 S=1（n2-1）+2 （n2-22）+3（n2-32）+n（n2-n2）解 S=n2（1+2+3+n）-（13+23+33+n3）文档编码:CC5C4W5P8H4 HL

21、1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O

22、3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL

23、1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O

24、3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL

25、1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O

26、3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL

27、1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3。-可编辑修改-（3）、倒序相加法适用于给定式子中与首末两项之和具有典型的规律的数列，采取把正着写与倒着写的两个和式相加，然后求和。例 10、求和：12363nnnnnSCCnC例 10、解0120363nnnnnnSCCCnC Sn=3n2n-1（4）、错位相减法如果一个数列是由一个等差数列与一个等比数列对应项相乘构成的，可把和式的两端同乘以上面的等比数列的公比，然后错位相减求和例 11、求数

28、列 1，3x，5x2,(2n-1)xn-1前 n 项的和解设 Sn=1+3+5x2+(2n-1)xn-1(2)x=0时，Sn=1(3)当 x0 且 x1 时，在式两边同乘以x 得 xSn=x+3x2+5x3+(2n-1)xn，-，得 (1-x)Sn=1+2x+2x2+2x3+2xn-1-(2n-1)xn(5)裂项法：把通项公式整理成两项(式多项)差的形式，然后前后相消。常见裂项方法：文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R

29、7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC

30、5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R

31、7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC

32、5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R

33、7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC

34、5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R

35、7 ZK8T1Q4F3O3。-可编辑修改-例 12、求和11111 53 75 9(21)(23)nn注：在消项时一定注意消去了哪些项，还剩下哪些项，一般地剩下的正项与负项一样多。在掌握常见题型的解法的同时，也要注重数学思想在解决数列问题时的应用。二、常用数学思想方法1函数思想运用数列中的通项公式的特点把数列问题转化为函数问题解决。【例 13】等差数列 an的首项 a10，前 n 项的和为Sn，若 Sl=Sk（l k）问 n 为何值时Sn最大？此函数以n 为自变量的二次函数。a10 Sl=Sk（l k），d0 故此二次函数的图像开口向下 f（l）=f（k）2方程思想【例 14】设等比数列 an

36、前 n 项和为 Sn，若 S3+S6=2S9，求数列的公比q。分析本题考查等比数列的基础知识及推理能力。解依题意可知q1。如果 q=1，则 S3=3a1，S6=6a1，S9=9a1。由此应推出a1=0 与等比数列不符。q1 整理得 q3（2q6-q3-1）=0 q0 文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:C

37、C5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7

38、R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:C

39、C5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7

40、R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:C

41、C5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7

42、R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3。-可编辑修改-此题还可以作如下思考：S6=S3+q3S3=（1+q3）S3。S9=S3+q

43、3S6=S3（1+q3+q6），由 S3+S6=2S9可得 2+q3=2（1+q3+q6），2q6+q3=03换元思想【例 15】已知 a，b，c 是不为 1 的正数，x，y，zR+，且求证：a，b，c 顺次成等比数列。证明依题意令ax=by=cz=k x=1ogak，y=logbk，z=logck b2=ac a，b，c 成等比数列（a，b，c 均不为 0）文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O

44、3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL

45、1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O

46、3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL

47、1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O

48、3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL

49、1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O

50、3。-可编辑修改-欢迎您的下载，资料仅供参考！致力为企业和个人提供合同协议，策划案计划书，学习课件等等打造全网一站式需求文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3文档编码:CC5C4W5P8H4 HL1T5H4Z7R7 ZK8T1Q4F3O3

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