1.
Sn×S(n-1)=2An=2(Sn-S(n-1))
两边除以Sn×S(n-1)
1=2(Sn-S(n-1))/(Sn×S(n-1))
1/S(n-1)-1/Sn=1/2
1/Sn-1/S(n-1)=-1/2
{1/Sn}是公差为-1/2的等差数列
2.
1/S1=1/A1=1/3
1/Sn=1/3+(n-1)×(-1/2)=(5-3n)/2
Sn=6/(5-3n)
n>=2时
An=Sn-S(n-1)=6/(5-3n)-6/(5-3(n-1))=18/((3n-5)(3n-8))
A1=3