An=2n-1,求证1/s1+1/s2+1/s3+…+1/sn
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An=2n-1,求证1/s1+1/s2+1/s3+…+1/sn
an=2n-1
Sn = a1+a2+...+an
= n^2
1/Sn = 1/n^2
for n>=2,
1/Sn < 1/[n(n-1)] = 1/(n-1) -1/n
1/S2+1/S3+...+1/Sn < 1 -1/n
1/S1+1/S2+...+1/Sn
=1 + [1/S2+...+1/Sn]
< 1 + (1- 1/n)
Sn = a1+a2+...+an
= n^2
1/Sn = 1/n^2
for n>=2,
1/Sn < 1/[n(n-1)] = 1/(n-1) -1/n
1/S2+1/S3+...+1/Sn < 1 -1/n
1/S1+1/S2+...+1/Sn
=1 + [1/S2+...+1/Sn]
< 1 + (1- 1/n)
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