Radius of convergence of $\sum_{n=1}^{\infty} (3^n +(-5)^n) x^{7n}$ What is the radius of convergence of the power series $\sum_{n=1}^{\infty} (3^n +(-5)^n) x^{7n}$?
I tried to find the limit of $\dfrac{a_{n+1}}{a_n}$ and I found it is $5$. Is that true, and does $x^{7n}$ play any role?

Change variable $y=x^7$, it would be easy to see the sum converges on 
$$
-\frac{1}{5}< y <\frac{1}{5}\iff-\frac{1}{\sqrt[7]{5}}< x <\frac{1}{\sqrt[7]{5}}
$$
So the convergence radius is $\frac{1}{\sqrt[7]{5}}$.
