∵n≥2时,an=Sn-Sn-1
∴由已知得,Sn2 =(Sn-Sn-1)(Sn-1)
整理得,Sn-Sn-1= -Sn·Sn-1
∴1/Sn - 1/Sn-1=(Sn-Sn-1)/ (Sn·Sn-1)= -1为常数,
∴数列{1/Sn}是等差数列,且首相为1,公差为-1.
∵n≥2时,an=Sn-Sn-1
∴由已知得,Sn2 =(Sn-Sn-1)(Sn-1)
整理得,Sn-Sn-1= -Sn·Sn-1
∴1/Sn - 1/Sn-1=(Sn-Sn-1)/ (Sn·Sn-1)= -1为常数,
∴数列{1/Sn}是等差数列,且首相为1,公差为-1.