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.