2022年数列公式及结论总结汇编 .pdf

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1、学习-好资料更多精品文档数列公式及结论总结1、等差等比数列相应结论等差数列等比数列通项公式dnaan)1(111nnqaa通项公式的推广式),()(Nnmdmnaamn),(Nnmqaamnmn性质若qpsr则qpsraaaa若qpsr则qpsraaaa等差（比）中项112nnnaaa112nnaaan数列的求和公式2)(1nnaanS或dnnnaSn2)1(1推导方法：倒序相加法.11)1(1)1(naqqqaSnn或)1()1(111qnaqqqaaSnn推导方法：错位相减法.2、等比数列性质应用时密切关注相应项下标和的关系.（1）若nnba,（项数相同）是等比数列，则)0(na，nnnn

2、nbabaaan,12仍是等比数列.（2）若数列naalog成等差数列，则数列na成等比数列.（3）若数列na成等差数列，则数列,32kmkmkmmaaaa仍是等比数列.学习-好资料更多精品文档（4）等比数列的单调性设na是等比数列，公比为q，则当101qa或1001qa时，数列na是递增数列；当1001qa或101qa时，数列na是递减数列；当1q时，数列na是常数列；当0q时，数列na是摆动数列，各项正负相间.3、等比数列和的性质若na是公比1q的等比数列，nS 为前n项和，则,232kkkkkSSSSS成公比为kq 的等比数列.4、由递推公式求数列通项公式类型方法nSfn（即：已知前 n

3、 项和 Sn 求na）2111nSSnSannnnTfn1112nnnTnaTnT文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文

4、档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10

5、文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F1

6、0文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F

7、10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10

8、F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G1

9、0F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G

10、10F10学习-好资料更多精品文档（即：已知前 n 项积 Tn 求na）1nnncaaad(0,0)cd取倒数变成1111nndac ac的形式)(1nfaann把原递推公式转化为)(1nfaann，利用累加法(逐差相加法)求解nnanfa)(1把原递推公式转化为)(1nfaann，利用累乘法(逐商相乘法)求解1nnakab设nam1()nk am，由 km-m=b求出 m的值，则数列1nnbbak是以 k 为公比的等比数列1nnnakap等式两边同时除以np：111nnnnaakppp；令nnnabp，则11nnkbbp；当1kp时，nb是以 1 为公差的等差数列；当1kp时，转化为类型一构

11、造等比数列；nnnqapaa12（其中 p，q 均为常数）把原递推公式转化为)(112nnnnaakaa，令qkpk，解得k,的值，借助数列nnaa1为等比数列，求得na通项5、常见数列的前n项和：2)1(321nnn；nnn22642；文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V

12、9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9

13、V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG

14、9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:C

15、G9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:

16、CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码

17、:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编

18、码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10学习-好资料更多精品文档2)12(531nn；6)12)(1(3212222nnnn；2233332)1()321(321nnnn.6、常用求和方法分组求和法把一个数列分成几个可以直接求和的数列的和（差）的形式.注意：公比用字母表示的等比数列要分类讨论.错位相减法适用于一个等差数列和一个等比数列（公比不等于1）对应项相乘构成的数列求和倒序相加法等差数列前n项和公式的推导方法一般适用于一个等差数列和一个等比数列的积所成数列并项求和法

19、把数列中若干项结合到一起，形成一个新的可求和的数列，此时，数列中若干项结合到一起，形成一个新的可求和的数列，此时，数列中的想可能正、负相间出现或呈现周期性.一般适用于符号数列n1或11n与阶差数列)(nf（)(nf为n的多项式）的积组成的数列裂项相消法又是把一个数列的通项公式分成两项差的形式，相加过程中消去中间项，只剩有限项再求和7、常见的裂项公式：111)1(1nnnn；文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T

20、6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3

21、T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A

22、3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5

23、A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O

24、5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1

25、O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU

26、1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10学习-好资料更多精品文档12112121)12)(12(1nnnn；nnnn111.文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU

27、1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 H

28、U1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10

29、HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10

30、 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J1

31、0 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J

32、10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10文档编码:CG9V9L1T4J10 HU1O5A3T6K1 ZU2R5P4G10F10