Question

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

⑴证明{1/Sn}是等差数列
⑵求Sn an

Answer 1

1
an=-SnSn-1
所以Sn-Sn-1=-SnSn-1
1（/Sn-1）-1/Sn=-1
1/Sn-1（/Sn-1）=1
所以{1/Sn}是等差数列
2
s1=a1=1/2
所以1/Sn=1/2+（n-1）=n+1/2
sn=1/(n+1/2)
再计算an =sn-sn-1就行了