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Question Number 31421 by abdo imad last updated on 08/Mar/18
$${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} {arctan}\left(\frac{\mathrm{3}}{\mathrm{9}{n}^{\mathrm{2}} −\mathrm{3}{n}−\mathrm{1}}\right). \\ $$
Answered by rahul 19 last updated on 08/Mar/18
$${use}\:{u}_{{n}} =\:\mathrm{3}{n}+\mathrm{1}\:{and}\:{v}_{{n}} =\:\mathrm{3}{n}−\mathrm{2}. \\ $$