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calculate-A-x-n-1-1-n-cos-nx-n-and-B-x-n-1-1-n-sin-nx-n-




Question Number 67521 by mathmax by abdo last updated on 28/Aug/19
calculate   A(x) =Σ_(n=1) ^∞   (((−1)^n  cos(nx))/n)  and B(x) =Σ_(n=1) ^∞  (((−1)^n  sin(nx))/n)
$${calculate}\:\:\:{A}\left({x}\right)\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} \:{cos}\left({nx}\right)}{{n}} \\ $$$${and}\:{B}\left({x}\right)\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} \:{sin}\left({nx}\right)}{{n}} \\ $$

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