I'm working on a problem where I need to show that the series of functions, f(x) = Ʃ (x(adsbygoogle = window.adsbygoogle || []).push({}); ^{n})/n^{2}, where n≥1, converges to some f(x), and that f(x) is continuous, differentiable, and integrable on [-1,1].

I know how to show that f(x) is continuous, since each f_{n}(x) is continuous, and I f_{n}(x) converges uniformly. Because each f_{n}(x) is also integrable, I can also show f(x) is integrable.

The trouble I'm having is proving that f(x) is differentiable. I need to show that the series of derivatives converges uniformly. However, I don't think I can use the Weierstrass M-Test in this scenario. Any ideas?

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# Differentiability of a Series of Functions

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