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Differentiability of $s=\sum\limits_{-\infty}^{\infty} {1\over (x-n)^2}$

Why is $f=\displaystyle\lim_{n\to\infty}f_n$ where $f_n=\displaystyle\sum_{k=-n}^n {1\over (x-k)^2}$ differentiable on $\mathbb R-\mathbb Z$? I know that the $f_n$'s are continuous and converge pointwise to $f$, but then it doesn't converge uniformly to $f$... so...?

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