Question: What is the domain of convergence of this power series: $$\sum\_{n>1}{\frac{n^2}{n!}x^n}$$
I tryed to calculate the radius, but I think that I did the limit wrong.

Answer: 
**Hint**. One may recall that each series that converges has its general term tending to $0$, here
$$
\lim\_{n \to \infty}(1.5)^n=? \qquad \lim\_{n \to \infty}\frac{4n-1}{5n+1}=?
$$ One may recall that the geometric series $\displaystyle \sum\_{n=0}^\infty x^n$ is convergent if and only if $|x|<1$. Concerning $A$, one may recall the nature of the [harmonic series](https://en.wikipedia.org/wiki/Harmonic_series_(mathematics)).
* A diverges as harmonic
* B divergent as geometric$(1.5>1)$
* C the general term doesn't go to zero
* D converges as geometric$(e^{-2}<1)$.