Question Number 202672 by BaliramKumar last updated on 31/Dec/23 $$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{the}\:\mathrm{divisors}\:\mathrm{of}\:\mathrm{24}\:\mathrm{is}\:\mathrm{60}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{the}\:\mathrm{divisors}\:\mathrm{of}\:\mathrm{24}×\mathrm{79}. \\ $$ Answered by a.lgnaoui last updated on 31/Dec/23 $$\mathrm{60} \\ $$ Commented…
Question Number 202698 by Bambamamoudou last updated on 31/Dec/23 $${determine}\:{le}\:{reste}\:{de}\:{la}\:{division}\:{eucludienne}\:{de}\:\mathrm{2023}^{\mathrm{2019}} {par}\:\mathrm{13} \\ $$ Answered by Rasheed.Sindhi last updated on 01/Jan/24 $$\because\:{gcd}\left(\mathrm{2023},\mathrm{13}\right)=\mathrm{1} \\ $$$$\therefore\:\:\:\:\mathrm{2023}^{\phi\left(\mathrm{13}\right)} \equiv\mathrm{1}\left({mod}\:\mathrm{13}\right) \\…
Question Number 202589 by mnjuly1970 last updated on 30/Dec/23 $$ \\ $$$$\:\:\Omega\:=\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{{k}}\:+\:\mathrm{2}{ln}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}{k}}\right)\right)=?\:\:\:\:\: \\ $$$$ \\ $$$$ \\ $$ Commented by mnjuly1970 last updated…
Question Number 202462 by pticantor last updated on 27/Dec/23 Answered by witcher3 last updated on 27/Dec/23 $$\mathrm{p}^{\mathrm{n}} −\mathrm{1}=\left(\mathrm{p}−\mathrm{1}\right)\left(\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}−\mathrm{1}} {\sum}}\mathrm{p}^{\mathrm{k}} \right) \\ $$$$\Rightarrow\mathrm{p}.\left(\mathrm{p}^{\mathrm{n}} \right)+\left(\mathrm{p}−\mathrm{1}\right).\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}−\mathrm{1}}…
Question Number 202376 by Engr_Jidda last updated on 25/Dec/23 Commented by Engr_Jidda last updated on 25/Dec/23 $${pls}\:{help}\:{my}\:{son}\: \\ $$ Commented by AST last updated on…
Question Number 202251 by BaliramKumar last updated on 23/Dec/23 $$\frac{\mathrm{1}}{\mathrm{1}×\mathrm{2}×\mathrm{3}}\:+\:\frac{\mathrm{1}}{\mathrm{2}×\mathrm{3}×\mathrm{4}}\:+\:\frac{\mathrm{1}}{\mathrm{3}×\mathrm{4}×\mathrm{5}}\:+\:…………..\:+\:\frac{\mathrm{1}}{\mathrm{n}\left(\mathrm{n}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{2}\right)}\:=\:?\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$ Commented by BaliramKumar last updated on 23/Dec/23 $$\frac{\mathrm{1}}{\mathrm{a}\left(\mathrm{a}+\mathrm{d}\right)\left(\mathrm{a}+\mathrm{2d}\right)}\:+\:\frac{\mathrm{1}}{\left(\mathrm{a}+\mathrm{d}\right)\left(\mathrm{a}+\mathrm{2d}\right)\left(\mathrm{a}+\mathrm{3d}\right)}\:+\:\:…….+\:\frac{\mathrm{1}}{\left\{\mathrm{a}+\left(\mathrm{n}−\mathrm{1}\right)\mathrm{d}\right\}\left\{\mathrm{a}+\mathrm{nd}\right\}\left\{\mathrm{a}+\left(\mathrm{n}+\mathrm{1}\right)\mathrm{d}\right\}}\:=\:? \\ $$ Commented by MATHEMATICSAM…
Question Number 202154 by cortano12 last updated on 22/Dec/23 $$\:\:\:\downharpoonleft\underline{\:} \\ $$ Commented by mr W last updated on 22/Dec/23 $$\mathrm{f}\left(\mathrm{xy}+\mathrm{1}\right)=\:\:\boldsymbol{\nu} \\ $$ Answered by…
Question Number 202183 by MathematicalUser2357 last updated on 22/Dec/23 $$\boldsymbol{{what}}\:\boldsymbol{{is}}\:\sqrt{\mathrm{2}}\:\boldsymbol{{over}}\:\mathrm{2} \\ $$ Commented by mr W last updated on 22/Dec/23 $${are}\:{you}\:{serious}? \\ $$ Answered by…
Question Number 202123 by BaliramKumar last updated on 21/Dec/23 $$\frac{\mathrm{1}}{\mathrm{1}×\mathrm{3}}\:+\:\frac{\mathrm{1}}{\mathrm{3}×\mathrm{5}}\:+\:\frac{\mathrm{1}}{\mathrm{5}×\mathrm{7}}\:+\:……………\infty\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated on 21/Dec/23 $${t}_{{n}} =\frac{\mathrm{1}}{\left(\mathrm{2}{n}−\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)} \\ $$$$\:\:\:\:\:{let}\:\:\frac{\mathrm{1}}{\left(\mathrm{2}{n}−\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)}=\frac{{a}}{\mathrm{2}{n}−\mathrm{1}}+\frac{{b}}{\mathrm{2}{n}+\mathrm{1}} \\ $$$$\:\:\:{a}\left(\mathrm{2}{n}+\mathrm{1}\right)+{b}\left(\mathrm{2}{n}−\mathrm{1}\right)=\mathrm{1}…
Question Number 202086 by necx122 last updated on 20/Dec/23 $${There}\:{are}\:{two}\:{possible}\:{routes}\:{from} \\ $$$${Zindhi}\:{to}\:{Katifa}.\:{One}\:{route}\:{is}\:{through} \\ $$$${Zindhi}/{Chadler}\:{expressway}\:{which}\:{is} \\ $$$$\mathrm{100}{km}\:{and}\:{the}\:{other}\:{is}\:{through}\:{Adfeti}\:{and} \\ $$$${Ngonu}\:{covering}\:{a}\:{distance}\:{of}\:\mathrm{80}{km}.\:{A} \\ $$$${motorist}\:{going}\:{through}\:{the}\:{expressway} \\ $$$${can}\:{travel}\:\mathrm{10}{km}/{h}\:{faster}\:{than}\:{the}\:{one} \\ $$$${going}\:{through}\:{Adfeti}\:{and}\:{Ngonu},\:{and} \\…