已知数列{an}的前n项和满足a1=1/2,an=-Sn*S(n-1),(n大于或等于2）,求an,Sn

an=Sn-Sn-1=-SnS(n-1)
(Sn-Sn-1)/[SnS(n-1)]=-1
1/S(n-1)-1/Sn=-1
1/Sn-1/S(n-1)=1,为定值.
1/S1=1/a1=1/(1/2)=2
数列{1/Sn}是以2为首项, 1为公差的等差数列.
1/Sn=1/S1+(n-1)=2+n-1=n+1
Sn=1/(n+1) S(n-1)=1/n
an=Sn-Sn-1=1/(n+1)-1/n
an=1/2 n=1
1/(n+1)-1/n n≥2
Sn=1/(n+1)