Find the radius of convergene R for power series For power series, find the radius of convergence R and determine if it is conditionally convergent, absolutely convergent, or divergent for $z = R$ and $z = −R$.
$\sum_{i=0}^{\infty} e^n z^n$
I'm trying to do root test, I think it is divergent as $C > 1$ but how do I find the radius of convergence R? 

$\sum e^n z^n = \sum (ez)^n$ is a geometric series and so converges iff $|ez|<1$. Therefore, $R=1/e$.
For $z=\pm R$, we get $\sum e^n(\pm 1)^n/e = \frac1e \sum (\pm e)^{n}$, which diverges absolutely  because $e>1$.
