# Thread: radius of convergence

1. ## radius of convergence

How do you find the radius of convergence for power series like the following:

$\displaystyle \sum_{n=1}^\infty (1/n!)*(z-1+i)^{2n}$

$\displaystyle \sum_{n=0}^\infty z^{2n+1}$

2. Originally Posted by grad444
$\displaystyle \sum_{n=1}^\infty (1/n!)*(z-1+i)^{2n}$
Hint: Use the fact that $\displaystyle (n!)^{1/n} \to \infty$ and now use the root test.

$\displaystyle \sum_{n=0}^\infty z^{2n+1}$
Again use the root test here.