Radius of Convergence for analytic functions I know that the radius of convergence of any power series can be found by simply using the root test, ratio test etc. 
I am confused as to how to find the radius of convergence for an analytic $f$ such as 
$f(z)=\frac{4}{(z-1)(z+3)}$. 
I can't imagine that I would have to find the power series representation of this, find the closed form, and then use one of the convergence tests. I am fairly certain that the radius of convergence would have to do with the singularities at $1$ and $-3$, however, I can't find a formula for the radius of convergence..

The power series for $f = \sum_{n=0}^{\infty}\frac{f^{(n)}(0)}{n!}z^{n}$ is guaranteed tdo have a radius of convergence $r=1$. The power series diverges for $|z| > 1$ and converges absolutely for $|z| < 1$ because of the singularity at $z=1$.
