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I-n-0-pi-4-1-cos-2n-1-x-dx-Prove-by-parts-that-2nI-n-2n-1-I-n-1-2-n-2-

Question Number 167740 by LEKOUMA last updated on 24/Mar/22 $${I}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{\mathrm{1}}{\mathrm{cos}\:^{\mathrm{2}{n}+\mathrm{1}} {x}}{dx} \\ $$$${Prove}\:{by}\:{parts}\:{that}: \\ $$$$\mathrm{2}{nI}_{{n}} =\left(\mathrm{2}{n}−\mathrm{1}\right){I}_{{n}−\mathrm{1}} +\frac{\mathrm{2}^{{n}} }{\:\sqrt{\mathrm{2}}} \\ $$ Terms of…

Question-36634

Question Number 36634 by tanmay.chaudhury50@gmail.com last updated on 03/Jun/18 Commented by Rasheed.Sindhi last updated on 03/Jun/18 $$\mathcal{T}{hank}\mathcal{S}\:{for}\:{sharing}!\:\mathrm{Are}\:\mathrm{there}\:\mathrm{only} \\ $$$$\mathrm{fibonacci}\:\mathrm{sequence}\:\mathrm{and}\:\mathrm{golden}\:\mathrm{ratio} \\ $$$$\mathrm{through}\:\mathrm{which}\:\mathrm{maths}\:\mathrm{is}\:\mathrm{related}\:\mathrm{to} \\ $$$$\mathrm{nature}?\mathrm{Any}\:\mathrm{other}\:\mathrm{numbers}\:\mathrm{like}\:\pi,{e} \\ $$$$\mathrm{present}\:\mathrm{in}\:\mathrm{nature}?…

Question-36626

Question Number 36626 by tanmay.chaudhury50@gmail.com last updated on 03/Jun/18 Commented by tanmay.chaudhury50@gmail.com last updated on 03/Jun/18 $${the}\:{vincci}\:{code}\:{is}\:{about}\:{golden}\:{ratio}..{see}\:{vdo} \\ $$$${in}\:{youtube}\:{to}\:{see}\:{the}\:{magic}.. \\ $$ Terms of Service Privacy…