Question

数列的前项和为Sn,a1=1,an=-3SnSn-1,n>=2求Sn

Answer 1

an=Sn-S(n-1)=-3SnS(n-1)

两边除以-SnS(n-1)

1/Sn-1/S(n-1)=3

所以1/Sn是等差数列,d=3

S1=a1=1

所以 1/Sn=1/S1+3(n-1)=3n-2

所以Sn=1/(3n-2)