Check whether the following series of function is uniformly convergent in $\Bbb R$. $$\sum_{n=1}^\infty (-1)^n \frac{x^2+n}{n^2}.$$ If the ddomain is any bounded interval then by Weierstrass M-test the series converges uniformly. But I am unable to check the uniform convergence when the domain is $\Bbb R$.
How to check ? Any hint. please?