证明:由题意可知:a(n+1)=S(n+1)-Sn(n+1 为下标 +2不是下标)
S(n+1)^2=(Sn+1+2)(Sn+1-Sn)=S(n+1)^2+2Sn+1-SnSn+1-2SnSn+1-2Sn
2Sn+1-2Sn=SnSn+1 两边同除以SnSn+1得
2/Sn-2/Sn+1=1 所以1/Sn+1-1/Sn=-1/2
综上数列{1/Sn}为等差数列
证明:由题意可知:a(n+1)=S(n+1)-Sn(n+1 为下标 +2不是下标)
S(n+1)^2=(Sn+1+2)(Sn+1-Sn)=S(n+1)^2+2Sn+1-SnSn+1-2SnSn+1-2Sn
2Sn+1-2Sn=SnSn+1 两边同除以SnSn+1得
2/Sn-2/Sn+1=1 所以1/Sn+1-1/Sn=-1/2
综上数列{1/Sn}为等差数列