How would I evaluate this limit? I have no idea how to evaluate this limit. Wolfram gives $0$, and I believe this, but I would like to see how it is done. The limit is
$$\lim_{n\rightarrow\infty}\frac{x^n}{(1+x)^{n-1}}$$
assuming $x$ is positive. Thanks in advance.

$\frac{x^n}{(1+x)^{n-1}} = \frac{x^n(1+x)}{(1+x)^{n}} = (\frac{x}{1+x})^{n}(1+x) = (\frac{x+1-1}{1+x})^{n}(1+x) = (1 - \frac{1}{1+x})^{n}(1+x)$
So taking the limit:
$\lim_{n\to\infty} \frac{x^n}{(1+x)^{n-1}} = \lim_{n\to\infty} (1 - \frac{1}{1+x})^{n}(1+x) = (1+x) * \lim_{n\to\infty} (1 - \frac{1}{1+x})^{n}$
Since $x>0$ we know $1 - \frac{1}{1+x} < 1$ therefore $\lim_{n\to\infty} (1 - \frac{1}{1+x})^{n} = 0$ giving us $(1+x)*0 = 0$
