E63 -- Demonstration de la somme de cette suite \( 1 + \frac{1}{4} + \frac{1}{9} + \frac{1}{16} +\) etc.

(Demonstration of the sum of the following series: \( 1 + \frac{1}{4} + \frac{1}{9} + \frac{1}{16} +\) etc.)


The answer hasn't changed; it's still \(\frac{\pi^2}{6}\). He does the sum of the odd square reciprocals by an arcsine integral, and considers the differential equation \((1-x^2)y''-xy'-1=0\).

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