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 $1 ,0 , 50 ,\frac{1}{50}$

Hint: $1 \leq d_n \leq n^{50}$. 
In other words $d_n$ is upper bounded by a power function of $n$. Try to use that when bounding $x^n$, which is an exponential function of $n$.
Another hint: For sufficiently large $n$, all $x<1$, and all $k$, one has $n^k<x^n$. In this case $k=50$. 
