已知数列an的前n项和为Sn,a1=2且Sn*Sn-1+1/2an=0
问题描述:
已知数列an的前n项和为Sn,a1=2且Sn*Sn-1+1/2an=0
1.求数an的前n项和Sn
2.求1/S1S2+1/S2S3+1/S3S4+...+1/S99S100-1/S100S101
答
Sn*Sn-1+1/2(Sn-Sn-1)=0 2=1/Sn-(1/Sn-1) 1/Sn是等差数列 首项为1/2 得1/Sn=(4n-3)/2 Sn=2/(4n-3) an=-2Sn*Sn-1=-8/((4n-3)(4n-7))