1. ## radius of convergence

I need to find the radius of convergence of the following power series, state the regions in which the series converge uniformly and study the convergence at the boundary of the interval of convergence?
How do i answer this and what is the answers i should get?

the sum of series k! from k=0 to infinity

any help would be appreciated

2. What you written is NOT a power series. A power series is of the form $\sum_{n=0}^\infty a_n x^n$.

What you have, $\sum_{k=0}^\infty k!$, has no variable and so none of the concepts of "radius of convergence", "uniform convergence", etc. apply. It is simply a numerical series that does not converge.

3. ## radius of convergence

sorry i meant to type it as you have. i have worked out this probelm but am stuck on a different one.
I need to find the radius of convergence of the following power series, state the regions in which the series converge uniformly and study the convergence at the boundary of the interval of convergence?
How do i answer this and what is the answers i should get?

the sum of power series [((n!)^2)/(2n!)] from k=1 to infinity