当n趋向无穷时,1/(n^2+1)+2/(n^2+2)+.......+n/(n^2+n)的极限是多少

如题所述

推荐答案推荐于2017-10-12

(1+2+……+n)/(n^2+n)<1/(n^2+1)+2/(n^2+2)+.......+n/(n^2+n)<(1+2+……+n)/(n^2+1)
1/2<1/(n^2+1)+2/(n^2+2)+.......+n/(n^2+n)<(n^2+n)/(2n^2+2)=(1+1/n)/(2+2/n^2）
当n趋向无穷时,1/(n^2+1)+2/(n^2+2)+.......+n/(n^2+n)的极限是1/2

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第1个回答 2011-01-11

利用夹逼性，所求式子大于（1+n）*n/2*(n^2+n)，小于（1+n）*n/2*(n^2+1)，两边的极限又都是1/2，所以所求极限也为1/2

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