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Question Number 34684 by math khazana by abdo last updated on 09/May/18
$${let}\:{U}_{{n}} =\:\frac{\pi}{\mathrm{4}}\:−\sum_{{k}=\mathrm{0}} ^{{n}} \:\frac{\left(−\mathrm{1}\right)^{{k}} }{\mathrm{2}{k}+\mathrm{1}} \\ $$$${calcilate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{U}_{{n}} \\ $$