Finding convergence zone/range for $\sum_{i=1}^\infty \frac{x^{n^2}}{n(n+1)}$ $$\sum_{i=1}^\infty \frac{x^{n^2}}{n(n+1)}$$
I used the ratio test and I end up with:
$$|x|*\frac{n}{n+2}$$
What steps do I need to take to continue?
Looking for hints or steps, not full solution/

Define 
$$
a_n=\begin{cases}0,\;\text{if n is not a perfect sqaure}\\
{1\over n+\sqrt{n}}, \text{otherwise}\end{cases}
$$
Your series is 
$$
\sum_{n}a_nx^n
$$
Now
$$
\limsup\sqrt[n]{|a_n|}=\lim_{n\to\infty}{1\over\sqrt[n]{n+\sqrt n}}
$$
Last hint:
$$n\le n+\sqrt n\le 2n$$
