若数列{an}的前n项和为Sn,且满足an+2SnSn-1=0(n≥2),a1=0.5,则Sn=________.

发布时间:2020-07-31 17:04:47

若数列{an}的前n项和为Sn,且满足an+2SnSn-1=0(n≥2),a1=0.5,则Sn=________.

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解析分析:由an=Sn-Sn-1,Sn-Sn-1+2SnSn-1=0,知,{}是等差数列,d=2.=2,.由此能求出Sn.

解答:an=Sn-Sn-1,Sn-Sn-1+2SnSn-1=0,∴,,∴{}是等差数列,d=2.=2,.∴.故
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