数列an首项a1=1前n项和sn与an之间满足an=2Sn^2/(Sn-1)(n大于等于2)
问题描述:
数列an首项a1=1前n项和sn与an之间满足an=2Sn^2/(Sn-1)(n大于等于2)
求证Sn是等差数列
答
2Sn(Sn-An)=-An
2SnSn-1=Sn-1-Sn
1/Sn-1/Sn-1=2
{1/Sn}便是一个等差数列,其首项为1/S1=1/A1=1/2
得出的结果便是:
Sn=2/(4n-3)
An=2/(4n-3)-2/(4n-7)