What would be the radius of convergence of $\sum\limits_{n=0}^{\infty} z^{3^n}$? I know how to find the radius of convergence of a power series $\sum\limits_{n=0}^{\infty} a_nz^n$, but how does this apply to the power series $\sum\limits_{n=0}^{\infty} z^{3^n}$? Would the coefficients $a_n=1$, so that one may apply D'Alembert's ratio test to determine the radius of convergence? I would appreciate any input that would be helpful.

The root test related formula for the radius of convergence $R$ is $\frac{1}{R}=\limsup\limits_{n\to\infty}\sqrt[n]{|a_n|}$.  Here $a_n$ is either $0$ or $1$ for each $n$.  Since it is $1$ infinitely many times, we see that the $\limsup$ is $1$.  
