若数列{an}中,an不等于0（n>=1),a1=1/2,前n项和Sn满足an=2Sn^2/2Sn-1,(n>=2),证明{1/Sn}是等差数列
人气：280 ℃ 时间：2019-08-21 12:09:19
解答
an=Sn-Sn-1an=2Sn^2/(2Sn-1)所以,代入移项得S(n-1)-Sn=2Sn*S(n-1)两边同除以Sn*S(n-1)便可得出1/Sn是等差数列 希望对你有帮助O(∩_∩)O
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