Tính \(\lim (\sqrt {{n^2} + 2n + 2} + n)\)

* Hướng dẫn giải

\(\begin{array}{l}\lim (\sqrt {{n^2} + 2n + 2} + n)\\ = \lim \dfrac{{2n + 2}}{{(\sqrt {{n^2} + 2n + 2} - n)}}\\ = \lim \dfrac{{2n + 2}}{{n\left( {\sqrt {1 + \dfrac{2}{n} + \dfrac{2}{{{n^2}}}} - 1} \right)}}\\ = \lim \dfrac{{2 + \dfrac{2}{n}}}{{\sqrt {1 + \dfrac{2}{n} + \dfrac{2}{{{n^2}}}} - 1)}}\\ = \dfrac{2}{0} = + \infty \end{array}\)