Find the interval of convergence of $x + \frac{1}{2} x^2 + 3x^3 + \frac{1}{4}x^4 +...$ How to find the interval of convergence of the following series: $x + \frac{1}{2} x^2 + 3x^3 + \frac{1}{4}x^4 +...$
I have no idea what to proceed. Any help? Thanks!

I would recommend splitting the $x^k*k$ and the $\frac{x^k}{k}$ terms and seeing where the two intervals intersect.
$(∑(2k+1)x^{2k+1}) + (∑\frac{x^{2k}}{2k})$
