(1/(n^2+n+1 ) +2/(n^2+n+2) +3/(n^2+n+3) ……n/(n^2+n+n)) 當N越于無窮大的極限

熱心網友

[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]?。ǎ迹奖硎拘∮诨虻扔冢? [n(n+1)]/[2(n^2+n+n)]與[n(n+1)]/[2(n^2+n+1]極限是1/2(n趨于無窮大) 由夾逼定理，原式的極限為１／２

熱心網友

已有高手做過,不再班門弄斧了

熱心網友

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.

熱心網友

答案是0