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
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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
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
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
(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
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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