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Show that the series \sum_{n=1}^{\infty} 1/(x^2 + n^2) defines a differentiable function f: R -> R...

Show that the series \sum_{n=1}^{\infty} 1/(x^2 + n^2) defines a differentiable function f: R -> R for which f' is continuous.

I'm thinking about using Cauchy Criterion to solve it, but I got stuck at trying to find the N such that the sequence of the partial sum from m+1 to n is bounded by epsilon

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