2022年数列通项公式和求和公式总结 .pdf
【一】求数列通项公式的常用方法各个求通项的方法之间并不是相互孤立的,有时同一题目中也可能同时用到几种方法,要具体问题具体分析!一 公式法数列符合等差数列或等比数列的定义,求通项时,只需求出1a与d或1a与q,再代入公式11naand或11nnaa q中即可.例1 数列na是等差数列,数列nb是等比数列,数列nc中对于任何*nN都有1234127,0,6954nnncabcccc分别求出此三个数列的通项公式.二 利用na与nS的关系如果给出条件是na与nS的关系式,可利用1112nnnSnaSSn求解.注意:应分1n和2n两种情况考虑,若两种情况能统一则应统一,否则应分段表示!例 2 若数列na的前n项和为33,2nnSa求na的通项公式.三 累加法形如已知1a且1nnaafn(f n为可求和的数列)的形式均可用累加法.例 3 数列na中已知111,2nnnaaan,求na的通项公式.四 累乘法形如已知1a且1nnafna(fn为可求积的数列)的形式均可用累乘法.例 4 数列na中已知1121,nnanaan,求na的通项公式.五 构造法若给出条件直接求na较难,可通过整理变形等从中构造出一个等差或等比数列,从而求出通项.常见的有形如1nnapaq(,p q为常数)且已知1a的数列可构造nac为等比数列求出nac,进而求出na.注意用待定系数法求常数c例 5 数列na中已知113,33nnaaa,求na的通项公式;数列na中已知2*121,2,21nnnSaannNS,求na的通项公式.数列na中已知0,nnaS是数列的前n项和,且12nnnaSa,求na的通项公式文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1【二】数列求和的常用方法数列求和关键入手点为求出通项公式并观察通项公式存在的特点而采取恰当的求和方法,另外各个方法之间并不是相互孤立的,有时同一题目中也可能同时用到几种方法,要具体问题具体分析!一 利用公式如果可判断出所求数列是等差或等比数列,则可直接利用公式求和.例 6 等比数列na的前n项和21nnS求2222123nnTaaaa的值.二 分组求和所求和的数列nc的通项公式可化成形如nnncab可采用分组求和.例 7 求数列3 9 251,2 482nn的前n项和.三 错位相减所求和的数列nc的通项公式可化成形如nnncab其中na,nb分别为等差和等比数列,可采用乘公比,错位相减.(等比数列的求和公式的推导过程)例 8 求和23230nnSxxxnxx文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1四 裂项相消常见裂项形式为11nan n,12121nann等.例 9 求和111114477103231nSnn五 倒序相加如果一个数列na,与其首末两项等距离的两项之和等于首末两项之和,可采用把正着写和倒着写的两个和式相加,就得到一个常数列的和,称为倒序相加.(等差数列的求和公式的推导过程)例 10 设442xxfx,求和122001200220022002Sfff文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 ZP8J3P7R9E1文档编码:CJ8S5F5F8X10 HR1N1T4I2P3 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