What can we say about the convergence of this series $$\sum {z^n\over n!} $$
I used Alembert's Ration test and get $$\lim_{n \infty}{u_n\over u_{n+1}}={n+1\over z}$$ As this tends to $\infty>1$ can i say that the given series is convergent for all values of $z$ ? 
Note : z is a complex number

The summation of the given series can be given as $e^z$ and hence the given series is convergent.
