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**[SOLVED] radius of convergence of an infinite summation**

## Homework Statement

find the radius of convergence of the series:

[tex]\sum\frac{(-1)^k}{k^2 3^k}(z-\frac{1}{2})^{2k}[/tex]

## Homework Equations

the radius of convergence of a power series is given by [tex]\rho=\frac{1}{limsup |c_k|^{1/k}}[/tex]

and is equal to [tex]\frac{1}{R}[/tex] when [tex]Lim_{n->\infty} \frac{|c_{k+1}|}{|c_k|}= R [/tex]

## The Attempt at a Solution

the major thing I'm stuck on is the '2k' in the series. General power series only have a factor 'k' in their powers, and I don't know how to get rid of it, so I can use the formula for radius of convergence of power series.