Convergence of $\sum_{k=0}^{\infty}{x^k\over (k+1)!}$ How can I prove the convergence of $$\sum_{k=0}^{\infty}{x^k\over (k+1)!}$$ 
and what is the limit function? I think that I need to use the fact that $\sum_{k=0}^{\infty}{x^k\over k!}$ is a convergent series. 
Any comments, suggestions or hints would be really appreciated 

Hint: notice that $\sum\limits_{k=0}^{\infty}\frac{x^k}{(k+1)!}=\frac{1}{x}\sum\limits_{k=0}^{\infty}\frac{x^{k+1}}{(k+1)!}=\frac{1}{x}\sum\limits_{k=1}^{\infty}\frac{x^k}{k!}$.
