已知数列的前n项和Sn满足an+2SnSn-1=0(n大于等于2)a1=1/2,n-1是下角标求an

an+2SnSn-1=0
Sn-Sn-1+2SnSn-1=0
1/Sn-1-1/Sn+2=0
1/Sn-1/Sn-1=2
{1/Sn}是以首项为1/a1=2
公差为2的等差数列
1/Sn=2+(n-1)*2=2n
Sn=1/2n
Sn-1=1/2(n-1)
an=1/2n-1/2(n-1)
=-1/2n(n-1)