Calculating the radius of convergence of a series. 
Let $d_n$ denote the number of divisors of $n^{50}$ then determine the radius of convergence of the series $\sum\limits_{n=1}^{\infty}d_nx^n$.

So obviously we need to calculate the limit of $\frac{d_{n+1}}{d_n}$. I am guessing I need some information about the asymptotic behavior of $d_n$. Any help?
The options given are $1 ,0 , 50 ,\frac{1}{50}$

Note that $d_1=1$, and for all $n \ge 2$, $d_n \le n^{50}$. So $$\frac{1}{R}=\limsup_{n \to \infty}{d_n}^{\frac{1}{n}}$$ and $$1 \le \limsup_{n \to \infty}{d_n}^{\frac{1}{n}} \le \lim_{n \to \infty}(n^{\frac{1}{n}})^{50}=1$$
