(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 (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

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

我同意刀歌的回答，是最好的

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)] (<=表示小于或等于) 趨于無窮大時,[n(n+1)]/[2(n^2+n+n)]和[n(n+1)]/[2(n^2+n+1)]的極限為1/2,故原式的極限為1/2

熱心網友

答案是0