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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

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Convergence of a power series

Let $s > 1$. Using Faulhaber's formula and some well known properties of the Bernoulli numbers, we have $$a_n = \frac{1}{n+1} \sum_{k = 0}^n 2^{-s} \left(\sum_{j = 0}^{+\infty} 2^{-(s+k-1) j}\right) \ …
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