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

* Hướng dẫn giải

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