I have to find the interval of uniform convergence, for the series
$$\sum_{n=1}^\infty \frac{n^2-n^4}{n^5+n^3+1}\left(x^2\sin\left(\frac{\pi x}{2}\right)\right)^n$$
Now my attempt has been to use the quotient (ratio) test to find the interval on which the series converges, so that I can find an upper bound. Taking the quotient test gives me the following:
$$\left|\frac{a_{n+1}}{a_n}\right|\rightarrow \left|x^2\sin\left(\frac{\pi x}{2}\right)\right|, n \rightarrow \infty$$
Therefore the series must be absolutely convergent on when $$\left|x^2\sin\left(\frac{\pi x}{2}\right)\right| < 1$$
However since this doesn't give me an upper bound, I'm stuck. The assignment offers me a few options to pick from, and there are no interval options above or below $\pm\sqrt{2}$, so I know that while there are intervals around all even numbers of $x$ these are not useful, though I do not know why. What am I missing?