How can i show that the series
$\sum_{n=1}^{\infty}\frac{x^{2n}}{(x+n)^{3/2}}$ is not uniformly convergent on $[1,\infty)$
I know that for given $\epsilon > 0$, we need to construct a sequence $x_n$ such that $|\frac{x^{2n}}{(x+n)^{3/2}}| > \epsilon$. The thing is I was not able to come up with such a sequence.