Question Number 128256 by Dwaipayan Shikari last updated on 05/Jan/21 $$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}!\mathrm{1}!}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{3}!\mathrm{2}!}\left(\frac{\mathrm{1}.\mathrm{3}}{\mathrm{2}^{\mathrm{2}} }\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{4}!\mathrm{3}!}\left(\frac{\mathrm{1}.\mathrm{3}.\mathrm{5}}{\mathrm{2}^{\mathrm{3}} }\right)^{\mathrm{2}} +….=\frac{\mathrm{4}}{\pi} \\ $$$${Prove}\:{the}\:{above}\:{Relation} \\ $$ Commented by Dwaipayan Shikari last…
Question Number 62712 by 30043018 last updated on 24/Jun/19 $$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 128236 by Dwaipayan Shikari last updated on 05/Jan/21 $$\frac{\mathrm{1}}{\mathrm{6}}\underset{{p}} {\overset{\infty} {\sum}}\frac{{logp}}{{p}^{\mathrm{2}} −\mathrm{1}}=\frac{{log}\mathrm{1}}{\pi^{\mathrm{2}} }+\frac{{log}\mathrm{2}}{\mathrm{4}\pi^{\mathrm{2}} }+\frac{{log}\mathrm{3}}{\mathrm{9}\pi^{\mathrm{2}} }+…\:\:\:\left({p}={prime}\right) \\ $$ Commented by Dwaipayan Shikari last updated…
Question Number 128197 by BHOOPENDRA last updated on 05/Jan/21 Commented by BHOOPENDRA last updated on 05/Jan/21 $${help}\:{me}\:{out}\:{this}? \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 128182 by BHOOPENDRA last updated on 05/Jan/21 Commented by BHOOPENDRA last updated on 05/Jan/21 $${find}\:{laplace}\:{transformation}? \\ $$ Answered by mathmax by abdo last…
Question Number 128126 by Agnibhoo last updated on 04/Jan/21 $$\:\frac{\mathrm{4}}{\mathrm{99}}\:+\:\frac{\mathrm{7}}{\mathrm{999}}\:+\:\frac{\mathrm{11}}{\mathrm{999999}}\:=\:? \\ $$ Answered by Geovanek last updated on 04/Jan/21 $$\frac{\mathrm{4}}{\mathrm{99}}\:+\:\frac{\mathrm{7}}{\mathrm{99}}\:+\:\frac{\mathrm{11}}{\mathrm{999999}}\:=\:{X} \\ $$$$\mathrm{We}\:\mathrm{can}\:\mathrm{see}\:\mathrm{that} \\ $$$$\frac{\mathrm{999999}}{\mathrm{99}}\:=\:\mathrm{10101}\:\:\:\boldsymbol{\mathrm{AND}} \\…
Question Number 128122 by Dwaipayan Shikari last updated on 04/Jan/21 $$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{16}}+\frac{\mathrm{5}^{\mathrm{2}} }{\mathrm{16}^{\mathrm{2}} .\mathrm{2}!}+\frac{\mathrm{5}^{\mathrm{2}} .\mathrm{9}^{\mathrm{2}} }{\mathrm{16}^{\mathrm{3}} .\mathrm{3}!}+\frac{\mathrm{5}^{\mathrm{2}} .\mathrm{9}^{\mathrm{2}} .\mathrm{13}^{\mathrm{2}} }{\mathrm{16}^{\mathrm{4}} .\mathrm{4}!}+…=\frac{\sqrt{\pi}}{\Gamma^{\mathrm{2}} \left(\frac{\mathrm{3}}{\mathrm{4}}\right)}={F}_{\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{4}},\frac{\mathrm{1}}{\mathrm{4}},\mathrm{1};\mathrm{1}\right) \\ $$$${Prove}\:{The}\:{above}\:{relation} \\…
Question Number 128112 by AgnibhoMukhopadhyay last updated on 04/Jan/21 $$\:\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}\:+\:\mathrm{4}\:+\:…..\:+\:\mathrm{100}\:=\:? \\ $$ Answered by Olaf last updated on 04/Jan/21 $$\mathrm{A}\:\left({n}+\mathrm{1}\right)×\left({n}+\mathrm{1}\right)\:\mathrm{squared}\:\mathrm{chess}\:\mathrm{board} \\ $$$$\mathrm{contains}\:\left({n}+\mathrm{1}\right)^{\mathrm{2}} \:\mathrm{squares}. \\ $$$$…
Question Number 128110 by Dwaipayan Shikari last updated on 04/Jan/21 $$\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \frac{{sinx}\:{sin}\left({x}+{y}\right)}{{x}\left({x}+{y}\right)}{dxdy} \\ $$ Answered by Olaf last updated on 04/Jan/21 $$\Omega\:=\:\int_{\mathrm{0}}…
Question Number 128093 by BHOOPENDRA last updated on 04/Jan/21 Answered by Dwaipayan Shikari last updated on 04/Jan/21 $$\mathscr{L}\left({e}^{\mathrm{2}{t}} +\mathrm{4}{t}^{\mathrm{3}} −\mathrm{2}{sin}\mathrm{3}{t}+\mathrm{3}{cos}\mathrm{3}{t}\right) \\ $$$$=\int_{\mathrm{0}} ^{\infty} {e}^{\mathrm{2}{t}−{st}} +\int_{\mathrm{0}}…