Question Number 86592 by M±th+et£s last updated on 29/Mar/20 $${prove}\:{that} \\ $$$$\mathrm{2}\underset{{x}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{2}^{{x}} \:\left({x}!\right)^{\mathrm{2}} }{\left(\mathrm{2}{x}\right)!\:\left({x}\right)} \\ $$ Commented by M±th+et£s last updated on 29/Mar/20…
Question Number 20927 by amaresh pradhan last updated on 08/Sep/17 $$\left({a}+{b}\right)×\left({a}+{b}\right) \\ $$ Answered by Joel577 last updated on 08/Sep/17 $$=\:\left({a}\:+\:{b}\right)^{\mathrm{2}} \:=\:{a}^{\mathrm{2}} \:+\:\mathrm{2}{ab}\:+\:{b}^{\mathrm{2}} \\ $$…
Question Number 20907 by DKumar last updated on 07/Sep/17 $${How}\:{many}\:{zeroes}\:\left(\mathrm{0}\right)\:{there}\:{in}\:\mathrm{1}×\mathrm{2}×\mathrm{3}×\mathrm{4}……….\mathrm{99}×\mathrm{100}\: \\ $$ Answered by dioph last updated on 07/Sep/17 $$\mathrm{zeros}\:\mathrm{in}\:\mathrm{number}\:=\:\mathrm{maximum}\:\mathrm{integer} \\ $$$${n}\:\mathrm{such}\:\mathrm{that}\:\mathrm{10}^{{n}} =\mathrm{2}^{{n}} \mathrm{5}^{{n}} \:\mathrm{divides}\:\mathrm{the}\:\mathrm{number}.…
Question Number 20827 by New Mathematics last updated on 04/Sep/17 $${find}\:{cube}\:{root}\:{of}\:\mathrm{12167}\:{by}\:{divison}\:{method}. \\ $$ Answered by Joel577 last updated on 04/Sep/17 $${I}\:{dont}\:{know}\:{about}\:{division}\:{method},\:{but} \\ $$$${I}\:{use}\:{this}\:{method} \\ $$$$\mathrm{12}.\mathrm{167}…
Question Number 20810 by Tinkutara last updated on 03/Sep/17 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{triples}\:\left({a},\:{b},\:{c}\right)\:\mathrm{of} \\ $$$$\mathrm{positive}\:\mathrm{integers}\:\mathrm{such}\:\mathrm{that} \\ $$$$\left(\mathrm{i}\right)\:{a}\:<\:{b}\:<\:{c}\:<\:\mathrm{10}\:\mathrm{and}\:\left(\mathrm{ii}\right)\:{a},\:{b},\:{c},\:\mathrm{10}\:\mathrm{form} \\ $$$$\mathrm{the}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{a}\:\mathrm{quadrilateral}? \\ $$ Commented by Tinkutara last updated on 04/Sep/17…
Question Number 86343 by jagoll last updated on 28/Mar/20 $$\mathrm{Dear}\:\mathrm{mr}\:\mathrm{w}.\:\mathrm{i}\:\mathrm{want}\: \\ $$$$\mathrm{discuss}\:\mathrm{for}\:\mathrm{equation} \\ $$$$\mathrm{find}\:\mathrm{minimum}\:\mathrm{and}\:\mathrm{maximum}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{xy}\:+\mathrm{2}\:\mathrm{with}\:\mathrm{constraint} \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}\:} =\:\mathrm{6}. \\ $$$$\mathrm{my}\:\mathrm{way}\:\left(\mathrm{short}\:\mathrm{cut}\right) \\ $$$$\Rightarrow\:\mathrm{x}^{\mathrm{2}} \:=\:\mathrm{y}^{\mathrm{2}}…
Question Number 151801 by ajfour last updated on 23/Aug/21 $${If}\:{a}\:{natural}\:{number}\:{of}\:\mathrm{3}\:{digit} \\ $$$$\left({for}\:{example}\right){N}={abc}\:\:{such}\:{that} \\ $$$${N}=\mathrm{100}{a}+\mathrm{10}{b}+{c}={a}!+{b}!+{c}! \\ $$$${Find}\:{all}\:{N}\:{of}\:{any}\:{number}\:{of} \\ $$$${digits}.\: \\ $$$${e}.{g}.\:\:{N}=\mathrm{1},\:\mathrm{2},\:\mathrm{145},\:… \\ $$ Terms of Service…
Question Number 20693 by Tinkutara last updated on 31/Aug/17 $$\mathrm{Integers}\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:….,\:{n},\:\mathrm{where}\:{n}\:>\:\mathrm{2},\:\mathrm{are} \\ $$$$\mathrm{written}\:\mathrm{on}\:\mathrm{a}\:\mathrm{board}.\:\mathrm{Two}\:\mathrm{numbers}\:{m},\:{k} \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{1}\:<\:{m}\:<\:{n},\:\mathrm{1}\:<\:{k}\:<\:{n}\:\mathrm{are} \\ $$$$\mathrm{removed}\:\mathrm{and}\:\mathrm{the}\:\mathrm{average}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{remaining}\:\mathrm{numbers}\:\mathrm{is}\:\mathrm{found}\:\mathrm{to}\:\mathrm{be}\:\mathrm{17}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{two} \\ $$$$\mathrm{removed}\:\mathrm{numbers}? \\ $$ Answered…
Question Number 151652 by ArielVyny last updated on 22/Aug/21 $${faire}\:{la}\:{division}\:{de}\:\left(\mathrm{1}−{x}^{{n}} \right)\:{par}\:\left(\mathrm{1}−{x}\right) \\ $$ Answered by puissant last updated on 22/Aug/21 $$=\mathrm{1}+{x}+{x}^{\mathrm{2}} +….+{x}^{{n}−\mathrm{1}} \\ $$ Commented…
Question Number 151641 by Tawa11 last updated on 22/Aug/21 Answered by Kamel last updated on 22/Aug/21 $${S}_{{n}} =\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\sum}}\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\mathrm{3}{k}} {dx}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}−{x}^{\mathrm{3}{n}}…