Question Number 173975 by savitar last updated on 22/Jul/22 $$ \\ $$$$\: \\ $$$$ \\ $$$$\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{{y}^{{a}−\mathrm{1}} }{\left(\mathrm{1}+{y}\right)^{{b}} }\:{dy}\:\overset{{u}=\frac{\mathrm{1}}{\mathrm{1}+{y}}} {=}\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\left(\mathrm{1}−{u}\right)^{{a}−\mathrm{1}} }{{u}^{{a}−\mathrm{1}} }\:{u}^{{b}}…
Question Number 108262 by 675480065 last updated on 15/Aug/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{y}^{\mathrm{y}} \right)^{\left(\mathrm{y}^{\mathrm{y}} \right)^{\left(\mathrm{y}^{\mathrm{y}} \right)} } \mathrm{dy}=? \\ $$$$\mathrm{please}\:\mathrm{help} \\ $$ Answered by mathdave last…
Question Number 42494 by Tawa1 last updated on 26/Aug/18 $$\mathrm{In}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{of}\:\mathrm{numbers}\:\:\mathrm{1},\:\mathrm{2},\:\mathrm{11},\:\mathrm{22},\:\mathrm{111},\:\mathrm{222},\:…\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits} \\ $$$$\mathrm{in}\:\mathrm{999th}\:\mathrm{terms}\:\mathrm{is}\:?? \\ $$ Commented by Tinku Tara last updated on 22/Apr/21 $$\mathrm{1st}\:\mathrm{term}\:\mathrm{1} \\ $$$$\mathrm{3rd}\:\mathrm{term}\:\mathrm{11}…
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Question Number 107844 by mr W last updated on 13/Aug/20 $${A}\:{general}\:{case}: \\ $$$${we}\:{have}\:{totally}\:{n}\:{letters},\:{among}\:{them} \\ $$$${n}_{\mathrm{1}} \:{times}\:{A},\:{n}_{\mathrm{2}} \:{times}\:{B},\:{n}_{\mathrm{3}} \:{times}\:{C}, \\ $$$${n}_{\mathrm{4}} \:{times}\:{D}\:{etc}. \\ $$$$\left({n}_{\mathrm{1}} ,{n}_{\mathrm{2}} ,{n}_{\mathrm{3}}…
Question Number 173354 by pete last updated on 10/Jul/22 $$\mathrm{A}\:\mathrm{three}−\mathrm{digit}\:\mathrm{odd}\:\mathrm{number}\:\mathrm{less}\:\mathrm{than}\:\mathrm{500} \\ $$$$\mathrm{is}\:\mathrm{to}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{from}\:\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4}\:\mathrm{and}\:\mathrm{5}.\:\mathrm{If}\:\mathrm{repetition} \\ $$$$\mathrm{of}\:\mathrm{digits}\:\mathrm{is}\:\mathrm{allowed},\:\mathrm{in}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways} \\ $$$$\mathrm{can}\:\mathrm{this}\:\mathrm{be}\:\mathrm{done}? \\ $$ Commented by pete last updated on 10/Jul/22…
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Question Number 42110 by rahul 19 last updated on 18/Aug/18 Commented by Tawa1 last updated on 19/Aug/18 $$\mathrm{sweet} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated…
Question Number 42106 by rahul 19 last updated on 18/Aug/18 Answered by tanmay.chaudhury50@gmail.com last updated on 18/Aug/18 $$\mathrm{5}{c}_{\mathrm{2}} ×\mathrm{2}!+\mathrm{5}{c}_{\mathrm{3}} ×\mathrm{3}!+\mathrm{5}{c}_{\mathrm{4}} ×\mathrm{4}!+\mathrm{5}{c}_{\mathrm{5}} ×\mathrm{5}! \\ $$$$=\mathrm{5}{p}_{\mathrm{2}} +\mathrm{5}{p}_{\mathrm{3}}…
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