数列{an}中,a1=1,2Sn^2=2anSn-an(n≥2,n属于N*),求an
人气:360 ℃ 时间:2020-04-22 15:24:18
解答
因 an=Sn-S(n-1)故 2Sn^2=(2Sn-1)(Sn-S(n-1))=2Sn^2-2SnS(n-1)-Sn+S(n-1)化简得:S(n-1)-Sn=2SnS(n-1)所以 1/Sn-1/S(n-1)=2即数列{1/Sn}是公差为2的等差数列所以 1/Sn=2n-1,Sn=1/(2n-1)所以 n≥2,n属于N*时 an=1/(2n...
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