Originally Posted by

**RaisinBread** Hey, I'm trying to show that the following sequence of functions

$\displaystyle f_n(x)=\sum_{k=1}^{n}\frac{1}{(x+k)^2}$

converges uniformly on $\displaystyle \mathbb{R}^+$.

To do that I'm trying to find the limit of the simple convergence of the sequence, I can easily show that the limit for the simple convergence exists by noticing that for every $\displaystyle x\in\mathbb{R}^+$,

$\displaystyle 0\leq\sum_{n=1}^{\infty}\frac{1}{(x+n)^2}\leq\sum_ {n=1}^{\infty}\frac{1}{n^2}$

and use the convergence of the Riemann Zeta Function. However I can't manage to what the function of the limit is.