(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(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
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(1/(n^2n1)2/(n^2n2)3/(n^2n3)……n/(n^2nn))当N越于无穷大的极限(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(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
(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
(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
(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(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
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^2 Lim{n→∞}(1+2+..+n)/(n^2+n+n)=Lim{n→∞}(1+2+..+n)/n^2=1/2==> Lim{n→∞}un=1/2.
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