Determine all the values of $x\in \mathbb{R}$ for which the series $\sum_{n=1}^\infty \frac{x^n}{1+n|x|^n}$ converges [closed]

Determine all the values of $x\in \mathbb{R}$ for which the series below converges$$\sum_{n=1}^\infty \frac{x^n}{1+n|x|^n} $$

This is a phd qualifying exam problem that I'm doing for practice. One of the suggested texts is Rudin's Principles of Mathematical Analysis, which is the one I'm using now. I want to know how to solve this question so hopefully I'll learn how to do it for the exam.