已知等差数列{an}的首项A1=3,2An=Sn·Sn-1(n>=2),求通项公式.已知等差数列{An}的首项A1=3,2An=Sn·Sn-1(n>=2),求{An}的通项公式.

问题描述:

已知等差数列{an}的首项A1=3,2An=Sn·Sn-1(n>=2),求通项公式.
已知等差数列{An}的首项A1=3,2An=Sn·Sn-1(n>=2),求{An}的通项公式.

2an=S(n)S(n-1)
2(Sn-Sn-1)=S(n)S(n-1)
2/Sn-1-2/Sn=1
1/Sn-1/Sn-1=-1/2
{1/Sn}是公差为-1/2的等差数列
1/Sn=1/S1-(n-1)/2
Sn=6/(5-3n)
Sn-1=6/(8-3n)