Interval and radius of convergence problem

[mooshupork34]

This problem is puzzling me so any help would be greatly appreciated!

Find the interval and the radius of convergence for the the following series.
a) The Maclaurin series for f(x)=xe^x

So far, I've multiplied the series for e^x by x and I've gotten:

x+x^2 +x^3/2! + x^4/3!...

However, I'm confused about what to do next....

 

[galactus]

See if it converges:

\(\displaystyle \L\\\sum_{n=1}^{\infty}\frac{x^{n}}{(n-1)!}\)