What is the value of $\sum_{n=0}^{\infty}\frac{(n+1)x^n}{n!}$? I need to find the value of the series $\sum_{n=0}^{\infty}\frac{(n+1)x^n}{n!}$.I've computed its radius of convergence which comes out to be zero.
I'm not getting how to make adjustments in the general terms of the series to get the desired result...

Hint
$$\dfrac{(n+1)x^n}{n!}=x\cdot\dfrac{x^{n-1}}{(n-1)!}+\dfrac{x^n}{n!}$$
Now $$e^y=\sum_{r=0}^\infty\dfrac{y^r}{r!}$$
