Find the radius of convergence of the given power series:
$$\sum _{n=1}^{ \infty} \frac{(-1)^n x^{5n+2}}{5n+2}$$
Through the ratio test, I can get it down to $$ \frac{(-1)^n+1 x^{5(n+1)+2}}{5(n+1)+2} /\frac{(-1)^n x^{5n+2}}{5n+2},$$ but then I am stuck.