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Generalization of Partial Sums of Harmonic Series

$\Huge{H_n = \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \cdots + \frac{1}{n} }$

$\Huge{H_z}$ is generalized harmonic series, such that:

$H_1 = 1$
$H_z = H_{z-1} + 1/z$

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Sum the series of reciprocal squares of the integers

In this post I will show one of methods of sum of $\sum\limits_{k=1}^\infty \dfrac{1}{k^2} .$

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Integral Problem 1:

$\LARGE{\int \sqrt{\dfrac{x}{1-x^3}} dx =?}$

Solution

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