数列{An}中,A1=1,n＞1,2Sn=2AnSn-An,求An
数列{An}中,A1=1,n＞1,2SnSn=2AnSn-An,求An
人气：140 ℃ 时间：2020-04-15 10:55:20
解答
2(Sn)^2=2anSn-an2(Sn)^2-2anSn=-an2Sn(Sn-an)=-an2Sn*S(n-1)=-an2Sn*S(n-1)=-[(Sn-S(n-1)]2=-1/S(n-1)+1/Sn 1/Sn -1/S(n-1)=2所以{1/Sn}是等差数列.S1=a1=11/Sn=1/a1+(n-1)d1/Sn=1/1+(n-1)*2 1/Sn=2n-1Sn=1/(2n-1)S...
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