Use a known Taylor Series to find the Taylor series about c=0 for the given function and find its radius of convergence.

$\displaystyle f(x)= cos x^3$

So, the existing Taylor series for cos(x) is

$\displaystyle \sum \frac{-1^k}{2k!}(x)^{2k}$

So the new Taylor Series for cos x^3 would be

$\displaystyle \sum \frac{-1^k}{2k!}(x)^{3k}$

Am I on the right track? And how do I find its radius of convergence?