Question Number 137347 by Dwaipayan Shikari last updated on 01/Apr/21 $$\frac{\mathrm{1}}{\mathrm{1}+\frac{\pi^{\mathrm{2}} }{\mathrm{1}+\frac{\left(\pi+\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{1}+\frac{\left(\pi+\mathrm{2}\right)^{\mathrm{2}} }{\mathrm{1}+…}}}}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\left(\pi+\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{1}+\frac{\left(\pi+\mathrm{2}\right)^{\mathrm{2}} }{\mathrm{1}+…}}}=\frac{\mathrm{1}}{\pi}\:\: \\ $$$$\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{or}}\:\boldsymbol{\mathrm{disprove}} \\ $$ Answered by MJS_new last updated…
Question Number 71809 by TawaTawa last updated on 20/Oct/19 Answered by tw000001 last updated on 21/Oct/19 $$\mathrm{I}\:\mathrm{have}\:\mathrm{showed}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{on}\:\mathrm{No}.\mathrm{71776}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 137341 by EDWIN88 last updated on 01/Apr/21 $$\int\:\frac{{dx}}{\mathrm{e}^{{x}/\mathrm{2}} +{e}^{{x}/\mathrm{3}} +{e}^{{x}/\mathrm{6}} +\mathrm{1}}\:=? \\ $$ Answered by liberty last updated on 01/Apr/21 Terms of Service…
Question Number 71806 by ahmadshahhimat775@gmail.com last updated on 20/Oct/19 Answered by MJS last updated on 20/Oct/19 $$\left(−\mathrm{2}\right)^{\sqrt{\mathrm{2}}} =\left(\mathrm{2e}^{\mathrm{i}\pi} \right)^{\sqrt{\mathrm{2}}} =\mathrm{2}^{\sqrt{\mathrm{2}}} \mathrm{e}^{\mathrm{i}\pi\sqrt{\mathrm{2}}} = \\ $$$$=\mathrm{2}^{\sqrt{\mathrm{2}}} \mathrm{cos}\:\pi\sqrt{\mathrm{2}}\:+\mathrm{2}^{\sqrt{\mathrm{2}}}…
Question Number 137340 by SLVR last updated on 01/Apr/21 Answered by SLVR last updated on 02/Apr/21 $${kindly}\:{provide}\:{the}\:{solution}\:{please} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 6268 by sanusihammed last updated on 21/Jun/16 $${Test}\:{for}\:{convergence}\:{of}\:{the}\:{series}\: \\ $$$$\infty \\ $$$$\Sigma\:\:\:\:\:\frac{{sin}\left({nx}\right)}{{n}^{\mathrm{2}} } \\ $$$${n}\:=\:\mathrm{1}\: \\ $$ Commented by FilupSmith last updated on…
Question Number 71802 by mathmax by abdo last updated on 20/Oct/19 $${find}\:\int\:\:\:\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\left({x}+\mathrm{3}\right)^{\mathrm{2}} \left({x}^{\mathrm{3}} −\mathrm{5}{x}+\mathrm{4}\right)}{dx} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 6267 by sanusihammed last updated on 21/Jun/16 $${Verify}\:{the}\:{convergence}\:{of}\:{the}\:{exponential}\:{series}\:\:{e}^{{x}} \\ $$$${using}\:{D}'{Alermbert}\:{ratio}\:{test}. \\ $$ Commented by Yozzii last updated on 21/Jun/16 $${u}_{{r}} =\frac{{x}^{{r}} }{{r}!}\Rightarrow\frac{{u}_{{r}+\mathrm{1}} }{{u}_{{r}}…
Question Number 137338 by liberty last updated on 01/Apr/21 $$\mathrm{Given}\:\frac{\mathrm{cos}\:\mathrm{8}\theta+\mathrm{6cos}\:\mathrm{6}\theta+\mathrm{13cos}\:\mathrm{4}\theta+\mathrm{8cos}\:\mathrm{2}\theta}{\mathrm{cos}\:\mathrm{7}\theta+\mathrm{5cos}\:\mathrm{5}\theta+\mathrm{8cos}\:\mathrm{3}\theta}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{then}\:\mathrm{what}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{tan}\:\mathrm{2}\theta\:? \\ $$ Answered by EDWIN88 last updated on 01/Apr/21 $$\mathrm{consider}\:\mathrm{numerator} \\ $$$$\Leftrightarrow\:\mathrm{cos}\:\mathrm{8}\theta+\mathrm{cos}\:\mathrm{6}\theta+\mathrm{5}\left(\mathrm{cos}\:\mathrm{6}\theta+\mathrm{cos}\:\mathrm{4}\theta\right)+\mathrm{8}\left(\mathrm{cos}\:\mathrm{4}\theta+\mathrm{cos}\:\mathrm{2}\theta\right) \\…
Question Number 71801 by mathmax by abdo last updated on 20/Oct/19 $${find}\:\:{I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{n}} \sqrt{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\:\:{with}\:{n}\:{integr}\:{natural} \\ $$ Terms of Service Privacy Policy Contact:…