Question

设S1=1+1/(1^2)+1/(2^2),S2=1+1/(2^2)+1/(3^2),S3=1+1/(3^2)+1/(4

Answer 1

√S1=1+1/(1×2) √S2=1+1/(2×3) ….√Sn=1+1/(n×(n+1))

S=(1+1+…..+1)+1/(1×2)+1/(2×3)+…+1/(n×(n+1))=n+[1-1/(n+1)]

= n+n/(n+1)

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