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Question Number 30177 by abdo imad last updated on 17/Feb/18
$${let}\:{x}\in{R}\:\:{and}\:{u}_{{n}} =\:\prod_{{k}=\mathrm{0}} ^{{n}} \:{cos}\left(\frac{{x}}{\mathrm{2}^{{k}} }\right)\:{find}\:{a}\:{simple}\:{form}\:{of} \\ $$$${u}_{{n}} . \\ $$
Answered by Tinkutara last updated on 18/Feb/18
$${u}_{{n}} =\frac{\mathrm{1}}{\mathrm{2}^{{n}+\mathrm{1}} }\mathrm{cosec}\left(\frac{\pi}{\mathrm{2}^{{n}} }\right) \\ $$