Hello everyone! I'm new here, this is my first post. I'm currently practicing some past examination papers, and I'm stuck on the following question:

**"Find the Taylor series of the function $\displaystyle e^z$ about the point z = 2, and state the radius of convergence of the power series."**
So far, I've found the Taylor series to be $\displaystyle \sum{e^2(z-2)^n/n!}$ (anybody know how to include the from n=0 to infinity part?)

I've looked at the radius of convergence pages on wikipedia and wolfram, but I'm a little shakey when it comes to understanding how to use the ratio test.

As stated on wikipidea (

Ratio test - Wikipedia, the free encyclopedia)

After working out $\displaystyle \frac{e^2(z-2)^{n+1}/(n+1)!}{e^2(z-2)^n/n!}$, I got $\displaystyle \frac{z-2}{(n+1)}$, so would I be correct in saying that the series converges for all z, since the limit of this function tends to zero as n tends to infinity?