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An=2n-1,求证1/s1+1/s2+1/s3+…+1/sn
人气:288 ℃ 时间:2020-06-10 05:31:32
解答
an=2n-1Sn = a1+a2+...+an = n^21/Sn = 1/n^2for n>=2,1/Sn < 1/[n(n-1)] = 1/(n-1) -1/n1/S2+1/S3+...+1/Sn < 1 -1/n1/S1+1/S2+...+1/Sn=1 +[1/S2+...+1/Sn]< 1 + (1- 1/n)
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