Limit as N goes to Infinity Consider this limit: $$\lim_{n\rightarrow\infty} \left( 1+\frac{1}{n} \right) ^{n^2} = x$$
I thought the way to solve this for $x$ was to reduce it using the fact that as $n \rightarrow \infty$, $\frac{1}{n} \rightarrow 0$:
$$\therefore \lim_{n\rightarrow\infty}(1+0)^{n^2} = x$$
Apparently this is wrong! Why is it wrong?

If your method isn't wrong so we have also
$$\lim_{n\to\infty}\frac{1}{n}\times n=\lim_{n\to\infty}0\times n=0???$$
