# Math Help - Series Convergence

1. ## Series Convergence

Find all x for which

$\displaystyle\sum\limits_{n=1}^\infty n^nx^n$

Attempt: Ratio Test

$\lim_{x \to +\infty} |\frac {(n+1)^{n+1}x^{n+1}}{n^nx^n}|$

$=(\frac{n+1}{n})^n(n+1)|x|$

$=(1+\frac{1}{n})^n(n+1)|x|$

$=e(n+1)|x|$

Where do I go from here?

2. For $x\neq 0$ we have

$\displaystyle\lim_{n\to +\infty}\left(1+\dfrac{1}{n}\right)^n(n+1)|x|=+\in fty$

So, the series is convergent iff $x=0$ .