已知数列An的前n项和为Sn.且满足an+2Sn*Sn-1=0=2>,a1=1/2,求证1/Sn是等差数列,求通项an的表达试_数学解答

已知数列An的前n项和为Sn.且满足an+2Sn*Sn-1=0=2>,a1=1/2,求证1/Sn是等差数列,求通项an的表达试

人气：207 ℃　时间：2020-06-28 04:08:13

解答

证明1/Sn等差数列,即证1/Sn - 1/Sn-1 =常数.当n=2时,a2+2(a1+a2)*a1=0,a2=-1/4,所以1/S2-1/S1=2.n>=2时,an=Sn-Sn-1带入an+2Sn*Sn-1=0得Sn-Sn-1+2Sn*Sn-1=0对此式两边同除以Sn*Sn-1,得1/Sn-1/Sn-1=2,得证...