(1/(n^2 n 1 ) 2/(n^2 n 2) 3/(n^2 n 3) ……n/(n^2 n n))

(1/(n^2+n+1 ) +2/(n^2+n+2) +3/(n^2+n+3) ……n/(n^2+n+n)) 当N越于无穷大的极限

热心网友

[n(n+1)]/[2(n^2+n+n)］<=(1/(n^2+n+1 ) +2/(n^2+n+2) +3/(n^2+n+3) ……n/(n^2+n+n))<=[n(n+1)]/[2(n^2+n+1]　（＜＝表示小于或等于） [n(n+1)]/[2(n^2+n+n)]与[n(n+1)]/[2(n^2+n+1]极限是1/2(n趋于无穷大) 由夹逼定理，原式的极限为１／２

热心网友

已有高手做过,不再班门弄斧了

热心网友

un=(1/(n^2+n+1 ) +2/(n^2+n+2) +3/(n^2+n+3) ……n/(n^2+n+n)),k/(n^2+n+n)≤k/(n^2+n+k)≤k/n^2==(1+2+..+n)/(n^2+n+n)≤un≤(1+2+..+n)/n^2Lim{n→∞}(1+2+..+n)/(n^2+n+n)=Lim{n→∞}(1+2+..+n)/n^2=1/2==Lim{n→∞}un=1/2.

热心网友

答案是0