prove-that-1-1-cosx-2-n-1-n-1-n-1-cos-nx-for-x-kpi-k-Z-

Tinku Tara June 4, 2023 Relation and Functions 0 Comments

Question Number 33985 by abdo imad last updated on 28/Apr/18

prove that (1/(1+cosx)) =2Σ_(n=1) ^∞ n(−1)^(n−1) cos(nx) for x≠kπ ,k∈ Z .

$${prove}\:{that}\:\frac{\mathrm{1}}{\mathrm{1}+{cosx}}\:=\mathrm{2}\sum_{{n}=\mathrm{1}} ^{\infty} {n}\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} {cos}\left({nx}\right)\:{for} \\ $$$${x}\neq{k}\pi\:,{k}\in\:{Z}\:. \\ $$

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