Question Number 45712 by malwaan last updated on 15/Oct/18 $$\mathrm{prove}\:\mathrm{that}\:: \\ $$$$\sqrt{\mathrm{2}}\:\mathrm{is}\:\mathrm{irrationl}\:\mathrm{number} \\ $$ Commented by maxmathsup by imad last updated on 15/Oct/18 $${let}\:{suppose}\:\sqrt{\mathrm{2}}=\frac{{p}}{{q}}\:{with}\:{p}\:{and}\:{q}\:{integrsn}\:{natural}\:{and}\:\Delta\left({p},{q}\right)=\mathrm{1}\:\Rightarrow \\…
Question Number 176774 by Ar Brandon last updated on 26/Sep/22 $$\mathrm{How}\:\mathrm{many}\:\mathrm{distinct}\:{y}\:\mathrm{exist}\:\mathrm{satisfying} \\ $$$$\mid{x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{18}\mid+\mid{y}−\mathrm{3}\mid=\mathrm{5} \\ $$ Answered by mr W last updated on 26/Sep/22 $${x},{y}\in\mathbb{Z}…
Question Number 111218 by Lekhraj last updated on 02/Sep/20 Answered by nimnim last updated on 02/Sep/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{8}\:\:\:\:\:\mathrm{3}\:\:\:\:\:\mathrm{1}\:\:\:\:\:\mathrm{1}\:\:\:\:\mathrm{9}\:\:\:\:\:\mathrm{9} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{8}\:\:\:\:\:\mathrm{3}\:\:\:\:\:\mathrm{1}\:\:\:\:\:\mathrm{1}\:\:\:\:\mathrm{9}\:\:\:\:\:\mathrm{9} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\:\:\:\:\:\:\mathrm{8}\:\:\:\:\:\mathrm{3}\:\:\:\:\:\mathrm{1}\:\:\:\:\:\mathrm{1}\:\:\:\:\mathrm{9}\:\:\:\:\:\mathrm{9} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}\:\:\:\:\:\mathrm{4}\:\:\:\:\:\mathrm{9}\:\:\:\:\:\mathrm{3}\:\:\:\:\:\mathrm{5}\:\:\:\:\mathrm{9}\:\:\:\:\:\mathrm{7}…
Question Number 45585 by pieroo last updated on 14/Oct/18 $$\mathrm{prove}\:\mathrm{that1}^{\mathrm{3}} +\mathrm{2}^{\mathrm{3}} +\mathrm{3}^{\mathrm{3}} +…+\mathrm{n}^{\mathrm{3}} =\frac{\mathrm{n}^{\mathrm{2}} \left(\mathrm{n}+\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{4}}\:\mathrm{for}\:\mathrm{every} \\ $$$$\mathrm{natural}\:\mathrm{number}\:\boldsymbol{\mathrm{n}} \\ $$ Commented by maxmathsup by imad…
Question Number 45410 by Rio Michael last updated on 12/Oct/18 $${given}\:{the}\:{AP} \\ $$$${a},{a}\:+{d}\:,{a}+\mathrm{2}{d},{a}+\mathrm{3}{d},… \\ $$$${show}\:{that}\: \\ $$$${S}_{{n}} =\:\frac{{n}}{\mathrm{2}}\left\{\left(\mathrm{2}{a}+\left({n}−\mathrm{1}\right){d}\right\}\right. \\ $$ Commented by maxmathsup by imad…
Question Number 45353 by pieroo last updated on 12/Oct/18 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{p}\left(\mathrm{n}\right)=\frac{\boldsymbol{\mathrm{a}}_{\mathrm{1}} +\boldsymbol{\mathrm{a}}_{\mathrm{2}} +…+\boldsymbol{\mathrm{a}}_{\mathrm{n}} }{\mathrm{n}}\:\geqslant\:^{\mathrm{n}} \sqrt{\boldsymbol{\mathrm{a}}_{\mathrm{1}} \boldsymbol{\mathrm{a}}_{\mathrm{2}} …\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} } \\ $$$$\forall\:\mathrm{n}\:\in\boldsymbol{\mathrm{N}} \\ $$ Commented by pieroo last…
Question Number 110815 by I want to learn more last updated on 30/Aug/20 Answered by mr W last updated on 30/Aug/20 $$\left({x}+{y}\right)^{\mathrm{3}} ={x}^{\mathrm{3}} +{y}^{\mathrm{3}} +\mathrm{3}{xy}\left({x}+{y}\right)…
Question Number 45224 by peter frank last updated on 10/Oct/18 Answered by MrW3 last updated on 10/Oct/18 $${N}=\mathrm{2}×\mathrm{3}×\mathrm{5}×\mathrm{7}+\mathrm{1}=\mathrm{211} \\ $$ Terms of Service Privacy Policy…
Question Number 176054 by BaliramKumar last updated on 11/Sep/22 $$\frac{\mathrm{1}}{\mathrm{2}!}\:+\:\frac{\mathrm{2}}{\mathrm{3}!}\:+\:\frac{\mathrm{3}}{\mathrm{4}!}\:+\:\frac{\mathrm{4}}{\mathrm{5}!}\:+\:………….\:\infty\:=\:? \\ $$ Answered by Ar Brandon last updated on 11/Sep/22 $${S}=\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{{n}−\mathrm{1}}{{n}!}=\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left({n}−\mathrm{1}\right)!}−\underset{{n}=\mathrm{2}}…
Question Number 44907 by byaw last updated on 06/Oct/18 Commented by byaw last updated on 11/Oct/18 $${please}\:{help} \\ $$ Terms of Service Privacy Policy Contact:…