(lim frac{{1 + 3 + 5 + ... + 2n + 1}}{{3{n^2} + 4}}) bằng

* Hướng dẫn giải

Ta có: \(1 + 3 + 5 + ... + \left( {2n + 1} \right) = \frac{{\left( {1 + 2n + 1} \right)\left( {n + 1} \right)}}{2} = {\left( {n + 1} \right)^2}\)

\(\lim \frac{{1 + 3 + 5 + ... + \left( {2n + 1} \right)}}{{3{n^2} + 4}} = \lim \frac{{{{\left( {n + 1} \right)}^2}}}{{3{n^2} + 4}} = \lim \frac{{1 + \frac{2}{n} + \frac{1}{{{n^2}}}}}{{3 + \frac{4}{{{n^2}}}}} = \frac{1}{3}\)