Question Number 11977 by 786786AM last updated on 08/Apr/17 $$\mathrm{If}\:\:{S}_{\mathrm{1}} ,\:{S}_{\mathrm{2}} ,\:{S}_{\mathrm{3}} \:\mathrm{be}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:{n},\:\mathrm{2}{n},\:\mathrm{3}{n}\:\mathrm{terms} \\ $$$$\mathrm{respectively}\:\mathrm{of}\:\mathrm{an}\:\mathrm{AP},\:\mathrm{then} \\ $$ Answered by ajfour last updated on 08/Apr/17 $${S}_{\mathrm{1}}…
Question Number 11943 by 010418 last updated on 06/Apr/17 $$\mathrm{The}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$${x}^{\mathrm{2}} +\:{x}\:+\:\mathrm{1}\:=\:\mathrm{1}\:\:\:\mathrm{is} \\ $$ Answered by ajfour last updated on 06/Apr/17 $$\Rightarrow\:{x}\left({x}+\mathrm{1}\right)=\mathrm{0} \\ $$$${this}\:{happens}\:{when}\:…
Question Number 11889 by murtaza8 last updated on 04/Apr/17 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in}\:\mathrm{which}\:\mathrm{8}\: \\ $$$$\mathrm{different}\:\mathrm{flowers}\:\mathrm{can}\:\mathrm{be}\:\mathrm{strung}\:\mathrm{to} \\ $$$$\mathrm{form}\:\mathrm{a}\:\mathrm{garland}\:\mathrm{so}\:\mathrm{that}\:\mathrm{4}\:\mathrm{particular} \\ $$$$\mathrm{flowers}\:\mathrm{are}\:\mathrm{never}\:\mathrm{separated}\:\mathrm{is} \\ $$ Answered by ajfour last updated on 04/Apr/17…
Question Number 11744 by mnbvcxz89 last updated on 30/Mar/17 $$\mathrm{If}\:\:\:\mathrm{5}^{\mathrm{n}+\mathrm{2}} =\:\mathrm{625}\:,\:\mathrm{find}\:\left[\mathrm{5}\left(\mathrm{n}+\mathrm{3}\right)\right]^{\mathrm{1}/{n}} . \\ $$ Answered by mrW1 last updated on 30/Mar/17 $$\mathrm{5}^{{n}+\mathrm{2}} =\mathrm{625}=\mathrm{5}^{\mathrm{4}} \\ $$$$\Rightarrow{n}+\mathrm{2}=\mathrm{4}…
Question Number 11737 by Tadagbé last updated on 30/Mar/17 $$\int\:\frac{\mathrm{1}}{{x}\left({x}^{{n}} +\mathrm{1}\right)}\:{dx}\:= \\ $$ Answered by ajfour last updated on 30/Mar/17 $${x}^{{n}} ={t}\:\:\:\Rightarrow\:{n}\mathrm{ln}\:{x}=\mathrm{ln}\:{t} \\ $$$$\frac{{ndx}}{{x}}=\frac{{dt}}{{t}} \\…
Question Number 11419 by fadim727 last updated on 25/Mar/17 $$\mathrm{If}\:\mathrm{A}\:=\:\left\{\mathrm{whole}\:\mathrm{numbers}\right\}\:\mathrm{and}\: \\ $$$$\mathrm{B}=\left\{\mathrm{natural}\:\mathrm{numbers}\right\},\:\mathrm{then}\:\mathrm{A}\bigtriangleup\mathrm{B}=\_\_\_. \\ $$ Commented by FilupS last updated on 26/Mar/17 $$\mathrm{whole}\:\mathrm{numbers}\:=\:\mathbb{Z}\:=\:\left\{…,\:−\mathrm{2},\:−\mathrm{1},\:\mathrm{0},\:\mathrm{1},\:\mathrm{2},\:…\right\} \\ $$$$\mathrm{natural}\:\mathrm{numbers}\:=\:\mathbb{N}\:=\:\left\{\mathrm{1},\:\mathrm{2},\:…\right\} \\…
Question Number 11267 by 786786AM last updated on 18/Mar/17 $$\mathrm{Sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{2}\:\mathrm{digit}\:\mathrm{numbers}\:\mathrm{which}\:\mathrm{when} \\ $$$$\mathrm{divided}\:\mathrm{by}\:\mathrm{4}\:\mathrm{yield}\:\mathrm{unity}\:\mathrm{as}\:\mathrm{remainder}\:\mathrm{is} \\ $$ Answered by mrW1 last updated on 19/Mar/17 $$\mathrm{13}+\mathrm{17}+\mathrm{21}+\centerdot\centerdot\centerdot+\mathrm{97} \\ $$$$=\frac{\mathrm{13}+\mathrm{97}}{\mathrm{2}}×\mathrm{22} \\…
Question Number 11246 by 786786AM last updated on 18/Mar/17 $$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:{n}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\:+\:\frac{\mathrm{3}}{\mathrm{4}}\:+\:\frac{\mathrm{7}}{\mathrm{8}}\:+\:\frac{\mathrm{15}}{\mathrm{16}}\:+\:…\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Answered by FilupS last updated on 18/Mar/17 $$\frac{\mathrm{1}}{\mathrm{2}}\:+\:\frac{\mathrm{3}}{\mathrm{4}}\:+\:\frac{\mathrm{7}}{\mathrm{8}}\:+\:\frac{\mathrm{15}}{\mathrm{16}}\:+\:…\:=\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{2}^{{k}} −\mathrm{1}}{\mathrm{2}^{{k}}…
Question Number 76774 by benjo 1/2 santuyy last updated on 30/Dec/19 $$\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{the}\:\mathrm{birth}\:\mathrm{days}\:\mathrm{of} \\ $$$$\mathrm{six}\:\mathrm{different}\:\mathrm{persons}\:\mathrm{will}\:\mathrm{fall}\:\mathrm{in}\:\mathrm{exactly} \\ $$$$\mathrm{two}\:\mathrm{calendar}\:\mathrm{months}\:\mathrm{is} \\ $$ Commented by mr W last updated on…
Question Number 76740 by benjo 1/2 santuyy last updated on 30/Dec/19 $$\mathrm{15}\:\mathrm{persons},\:\mathrm{among}\:\mathrm{whom}\:\mathrm{are}\:{A}\:\mathrm{and}\:{B}, \\ $$$$\mathrm{sit}\:\mathrm{down}\:\mathrm{at}\:\mathrm{random}\:\mathrm{at}\:\mathrm{a}\:\mathrm{round}\:\mathrm{table}. \\ $$$$\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{there}\:\mathrm{are}\:\mathrm{4}\:\mathrm{persons} \\ $$$$\mathrm{between}\:{A}\:\mathrm{and}\:{B}\:\mathrm{is} \\ $$ Commented by mr W last…