Here's another limit:

$\displaystyle

\lim_{n\to \infty}\left(\frac{n^2+2}{2n^2+1}\right)^{n^2}

$

That's all I could get from it:

$\displaystyle

\lim_{n\to \infty}\frac{\left(1+\frac{2}{n^2}\right)^{n^2}}{2 ^{n^2}\left(1+\frac{1}{2n^2}\right)^{n^2}}

$

And everything would be quite fine if there was no $\displaystyle 2^{n^2}$.... Then the limit would be $\displaystyle e^\frac{3}{2}$, just like the answers say.... Am I wrong somewhere, or is there a mistake in this example?

Thank you in advance.