What is the radius of convergence of $\sum_{k\geq 0}3^{k^2}x^{k^2}$.
MY TRIAL Using Cauchy's root test $$\limsup\limits_{k\to\infty}\sqrt[k]{3^{k^2}}=\limsup\limits_{k\to\infty}3^k=\infty.$$
So, radius of convergence is $0.$ Kindly check, I'm I right?