设数列{an}的前n项和为Sn,且满足Sn-Sn-1+2SnSn-1=0(n≥2)设数列{an}的前n项和为Sn,且满足Sn-S(n-1)+2SnS(n-1)=0(n≥2),a1=1/2.1 求证,数列{1/Sn}是等差数列 2 求an的通项公式

问题描述:

设数列{an}的前n项和为Sn,且满足Sn-Sn-1+2SnSn-1=0(n≥2)
设数列{an}的前n项和为Sn,且满足Sn-S(n-1)+2SnS(n-1)=0(n≥2),a1=1/2.
1 求证,数列{1/Sn}是等差数列 2 求an的通项公式