Tính lim frac1 + 2 + 3 + ... + n2n2.

$\lim \frac{{1 + 2 + 3 + ... + n}}{{2{n^2}}} = \lim \frac{{\frac{{n\left( {n + 1} \right)}}{2}}}{{2{n^2}}} = \lim \frac{{{n^2} + n}}{{4{n^2}}} = \frac{1}{4}$.