已知数列{an}的前n项和为Sn,且满足an+2Sn+Sn-1=0(n≥2),a1+1/2

问题描述:

已知数列{an}的前n项和为Sn,且满足an+2Sn+Sn-1=0(n≥2),a1+1/2
(1)求证:{1/Sn}是等差数列
(2)求an的表达式
关系式是an+2Sn*Sn-1=0

应该是a1=0.5吧.(1)先把a1转化,Sn-(Sn-1)+2Sn*Sn-1=0,(Sn-1)-Sn=2Sn*Sn-1因为Sn不为0,所以两边同除Sn*Sn-1可得1/Sn-1/(Sn-1)=2很明显,{1/Sn}是等差数列公差是2(2)可求出1/Sn=2n,n属于N*.所以Sn=1/2nan=Sn-...