Question Number 798 by 123456 last updated on 15/Mar/15 $$\sqrt{\mathrm{1}+\mathrm{2}\sqrt{\mathrm{1}+\mathrm{3}\sqrt{\mathrm{1}+\mathrm{4}\sqrt{\mathrm{1}+\centerdot\centerdot\centerdot}}}} \\ $$ Answered by prakash jain last updated on 15/Mar/15 $$\mathrm{Ramanujan}'{s}\:\mathrm{Formula} \\ $$$${x}+\mathrm{1}=\sqrt{\mathrm{1}+{x}\sqrt{\mathrm{1}+\left({x}+\mathrm{1}\right)\sqrt{\mathrm{1}+\left({x}+\mathrm{2}\right)\sqrt{\mathrm{1}+…}}}} \\ $$$$\mathrm{For}\:{x}=\mathrm{2}…
Question Number 66332 by mathmax by abdo last updated on 12/Aug/19 $${let}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{{n}} \sqrt{\mathrm{1}−{x}}{dx} \\ $$$$\left.\mathrm{1}\right){calculate}\:{A}_{\mathrm{0}} \:{and}\:{A}_{\mathrm{1}} \\ $$$$\left.\mathrm{2}\right){prove}\:{that}\:\forall{n}\in{N}^{\bigstar} \:\:\:\:\left(\mathrm{3}+\mathrm{2}{n}\right){A}_{{n}} =\mathrm{2}{nA}_{{n}−\mathrm{1}} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{A}_{{n}}…
Question Number 131865 by mohammad17 last updated on 09/Feb/21 $${sin}\left(\mathrm{3}{x}\right){sin}\left(\mathrm{5}{x}\right){sin}\left(\mathrm{7}{x}\right){sin}\left(\mathrm{9}{x}\right) \\ $$ Commented by guyyy last updated on 12/Feb/21 Commented by guyyy last updated on…
Question Number 66330 by mathmax by abdo last updated on 12/Aug/19 $${let}\:{I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{{n}} \:{e}^{−{x}} \:{dx}\:\:\:\:{with}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{I}_{\mathrm{0}} \:,\:{I}_{\mathrm{1}} \:{and}\:{I}_{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right){find}\:{arelation}\:{between}\:{I}_{{n}} \:{and}\:{I}_{{n}} \\…
Question Number 795 by malwaan last updated on 15/Mar/15 $${what}\:{is}\:{the}\:{last}\:{digit}\:{of} \\ $$$$\mathrm{7}^{\left(\mathrm{7}^{\left(\mathrm{7}….\right)} \right)} \: \\ $$$${the}\:{number}\:{of}\:\mathrm{7}'{s}\:{is}\:\mathrm{1001} \\ $$ Answered by prakash jain last updated on…
Question Number 66328 by mathmax by abdo last updated on 12/Aug/19 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{dt}}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)^{\mathrm{3}} } \\ $$ Commented by mathmax by abdo last updated…
Question Number 131866 by mnjuly1970 last updated on 09/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{advanced}\:\:\:{calculus}… \\ $$$$\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} \frac{{dx}}{{x}^{\mathrm{5}} \left({e}^{\frac{\mathrm{1}}{{x}}} −\mathrm{1}\right)}=? \\ $$$$ \\ $$ Answered by mnjuly1970 last updated…
Question Number 66326 by mathmax by abdo last updated on 12/Aug/19 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{x}^{\mathrm{4}} \:+\mathrm{1}}{{x}^{\mathrm{6}} +\mathrm{1}}{dx} \\ $$ Commented by Prithwish sen last updated on…
Question Number 131860 by aurpeyz last updated on 09/Feb/21 $${what}\:{is}\:{the}\:{magnitude}\:{and}\:\: \\ $$$${direction}\left({in}\:{degree}\right)\:{of}\:{this}\:{vector}? \\ $$$${F}=−\mathrm{3}×\mathrm{10}^{−\mathrm{6}} {i}−\mathrm{13}.\mathrm{35}×\mathrm{10}^{−\mathrm{6}} {j} \\ $$$$\left({a}\right)\:\mathrm{282}.\mathrm{5}^{\mathrm{0}} \:\left({b}\right)\mathrm{78}.\mathrm{5}^{\mathrm{0}} \:\left({c}\right)\:\mathrm{82}.\mathrm{5}^{\mathrm{0}} \:\left({d}\right)\mathrm{78}.\mathrm{5}^{\mathrm{0}} \\ $$$$\left({e}\right)\mathrm{282}.\mathrm{5}^{\mathrm{0}} \\ $$…
Question Number 66324 by mathmax by abdo last updated on 12/Aug/19 $${find}\:{nature}\:{of}\:{the}\:{serie}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} }{\mathrm{2}^{{n}} \:+{ln}\left({n}\right)} \\ $$ Commented by mathmax by abdo last updated…