I have come across a problem involving the radius of convergence of power series that I can't solve for the life of me, any help would be greatly appreciated. I cannot use the lim sup method to solve this.
The problem is as follows.
Prove that if $\sum_{n=0}^\infty a_nx^n$ has radius of convergence $R_1 > 1$ and $\sum_{n=0}^\infty b_n x^n$ has radius of convergence $R_2 > 1$ then the radius of convergence R of $\sum_{n=0}^\infty a_nb_nx^n$ is at least $R_1R_2$
Thank you.