# Complex Analysis: Radius of Convergence

## Homework Statement

Find the radius of convergence of the power series:
a) $$\sum$$ z$$^{n!}$$
n=0 to infinity

b) $$\sum$$ (n+2$$^{n}$$)z$$^{n}$$
n=0 to infinity

## The Attempt at a Solution

a) Is cn in this case just 1? And plugging it in, the radius is 1?

b) cn = n+2$$^{n}$$, so then limsup n=> infinity |n+2$$^{n}$$|$$^{1/n}$$ => ?? I'm stuck at this point.

i'm also confused in general, is cn just a sequence of coefficients, and what is zn? And I have other formulas for figuring out the radius of convergence, such as the ratio test. I'm not sure when to use which methods. Thank you!