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

学习时间:2026-03-30 11:50:24 阅读：6459

设S1=1+1/(1^2)+1/(2^2),S2=1+1/(2^2)+1/(3^2),S3=1+1/(3^2)+1/(4^2).Sn=1+1/[n^2+1/(n+1)^2].设S=√S1+√S2+√S3+.+√Sn,则S=?(用含n的代数式表示,其中n为正整数）

拼搏的御姐

2026-03-30 11:50:24

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√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) 点点外婆祝你学习进步