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find-the-value-of-n-1-cos-npix-n-2-with-0-lt-x-lt-1-




Question Number 28879 by abdo imad last updated on 31/Jan/18
find the value of Σ_(n=1) ^(+∞)   ((cos(nπx))/n^2 ) with  0<x<1.
$${find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{1}} ^{+\infty} \:\:\frac{{cos}\left({n}\pi{x}\right)}{{n}^{\mathrm{2}} }\:{with}\:\:\mathrm{0}<{x}<\mathrm{1}. \\ $$

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