Question Number 111466 by Dwaipayan Shikari last updated on 03/Sep/20 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}^{{n}} }{{n}!} \\ $$ Commented by Her_Majesty last updated on 03/Sep/20 $${for}\:{large}\:{n}:\:{n}!\approx{n}^{{n}} {e}^{−{n}}…
Question Number 111450 by Dwaipayan Shikari last updated on 03/Sep/20 Commented by Dwaipayan Shikari last updated on 03/Sep/20 $${Kindly}\:{check}\:{it} \\ $$$${I}\:{have}\:{found}\:{this}\:{while}\:{experimenting} \\ $$ Terms of…
Question Number 111428 by Dwaipayan Shikari last updated on 03/Sep/20 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}^{\mathrm{3}} }{{n}!} \\ $$ Commented by Dwaipayan Shikari last updated on 03/Sep/20 $$…
Question Number 176895 by Mastermind last updated on 27/Sep/22 $$\mathrm{7C}=\mathrm{log}_{\mathrm{2}} \frac{\mathrm{1}}{\mathrm{6}}+\mathrm{log}_{\mathrm{3}} \mathrm{27} \\ $$$$ \\ $$$$\mathrm{Solve} \\ $$ Answered by BaliramKumar last updated on 27/Sep/22…
Question Number 45688 by last updated on 15/Oct/18 $$\int\frac{\mathrm{1}}{{sinxcos}^{\mathrm{2}} {x}}{dx}=? \\ $$ Commented by maxmathsup by imad last updated on 15/Oct/18 $${let}\:{I}\:=\int\:\:\:\:\frac{{dx}}{{sinx}\:{cos}^{\mathrm{2}} {x}}{dx}\:\:{we}\:{have}\:{I}\:=\:\int\:\frac{\mathrm{1}+{tan}^{\mathrm{2}} {x}}{{sinx}}{dx}\:\:{changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}…
Question Number 45635 by maxmathsup by imad last updated on 14/Oct/18 $$\left.\mathrm{1}\right){find}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{xt}^{\mathrm{3}} \right){dt}\:\:{with}\:\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{2}+{t}^{\mathrm{3}} \right){dt}\:. \\ $$ Commented by maxmathsup…
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Question Number 111132 by bemath last updated on 02/Sep/20 $$\mathrm{prove}\:\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction} \\ $$$$\Rightarrow\:\mathrm{7}^{\mathrm{n}} −\left(\mathrm{3n}+\mathrm{4}\right)×\mathrm{4}^{\mathrm{n}−\mathrm{1}} \:\mathrm{divided}\:\mathrm{by}\:\mathrm{9} \\ $$ Answered by john santu last updated on 02/Sep/20 $${let}\:{p}\left({n}\right)\:=\:\mathrm{7}^{{n}}…
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Question Number 111080 by bemath last updated on 02/Sep/20 $$\:\:\sqrt{\mathrm{bemath}} \\ $$$$\left(\mathrm{1}\right)\underset{\mathrm{k}=\mathrm{50}} {\overset{\mathrm{100}} {\sum}}\:\frac{\mathrm{1}}{\mathrm{k}\left(\mathrm{151}−\mathrm{k}\right)}\:? \\ $$$$\left(\mathrm{2}\right)\:\mathrm{without}\:\mathrm{L}'\mathrm{Hopital}\:\mathrm{and}\:\mathrm{series}\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{xcos}\:\mathrm{x}−\mathrm{sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{2}} \mathrm{sin}\:\mathrm{x}} \\ $$ Answered by john…