Práctica 3 ejercicio 9m

EJERCICIO 9: ...

(m) $ \left( \dfrac{n^2 +2}{5n^2+3} \right)^{1/n}$

Solución:
$ \lim\limits_{n\to \infty} \left( \dfrac{n^2 +2}{5n^2+3} \right)^{1/n} =
\lim\limits_{n\to \infty} \left( \dfrac{\cancel{n^2}\left(1+\dfrac{2}{n^2}\right)}{\cancel{n^2}\left(5+\dfrac{3}{n^2}\right)} \right)^{1/n} = $

$\lim\limits_{n\to \infty} \left(\dfrac{1+\dfrac{2}{n^2}}{5+\dfrac{3}{n^2}}\right)^{1/n} = 1$