Question Number 144928 by ArielVyny last updated on 30/Jun/21 $$\underset{{n}\geqslant\mathrm{0}} {\sum}\frac{\left(−\mathrm{1}\right)^{{n}} }{\left({n}+{z}\right){n}!} \\ $$ Answered by Dwaipayan Shikari last updated on 01/Jul/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \underset{{n}\geqslant\mathrm{0}}…
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Question Number 78979 by jagoll last updated on 22/Jan/20 $$\mathrm{the}\:\mathrm{first}\:\mathrm{n}\:\mathrm{even} \\ $$$$\mathrm{numbers}\:\mathrm{are}\:\mathrm{known}.\:\mathrm{if}\:\mathrm{one}\:\mathrm{number} \\ $$$$\mathrm{is}\:\mathrm{deleted}\:\mathrm{then}\:\mathrm{the}\:\mathrm{average} \\ $$$$\mathrm{of}\:\mathrm{remaining}\:\mathrm{numbers}\:\mathrm{is}\:\frac{\mathrm{2582}}{\mathrm{50}}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{deleted}\:\mathrm{number}. \\ $$ Commented by mr W last…
Question Number 144482 by ArielVyny last updated on 25/Jun/21 $${show}\:{that}\:\forall{n}\in\mathbb{Z}\: \\ $$$${E}\left(\frac{{n}−\mathrm{1}}{\mathrm{2}}\right)+{E}\left(\frac{{n}+\mathrm{2}}{\mathrm{4}}\right)+{E}\left(\frac{{n}+\mathrm{4}}{\mathrm{4}}\right)={n} \\ $$ Answered by Olaf_Thorendsen last updated on 25/Jun/21 $${x}\:=\:\mathrm{E}\left(\frac{{n}−\mathrm{1}}{\mathrm{2}}\right)+\mathrm{E}\left(\frac{{n}+\mathrm{2}}{\mathrm{4}}\right)+\mathrm{E}\left(\frac{{n}+\mathrm{4}}{\mathrm{4}}\right) \\ $$$$\mathrm{1st}\:\mathrm{case}\::\:{n}\:=\:\mathrm{4}{p} \\…
Question Number 144460 by byaw last updated on 25/Jun/21 $$ \\ $$$$\mathrm{If}\:\mathrm{C}=\mathrm{226}{k}\:\mathrm{find}\:\mathrm{the}\:\mathrm{least} \\ $$$$\mathrm{integal}\:\mathrm{value}\:\mathrm{of}\:{k}\:\mathrm{that}\:\mathrm{will} \\ $$$$\mathrm{make}\:\mathrm{C}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{square} \\ $$ Answered by Rasheed.Sindhi last updated on 26/Jun/21…
Question Number 13346 by tawa tawa last updated on 19/May/17 Commented by ajfour last updated on 19/May/17 $${your}\:{previous}\:{question}\:{Q}\mathrm{13345} \\ $$$${something}\:{wrong}\:{uploading}\:{it}. \\ $$$${cannot}\:{click}\:{to}\:{answer}.. \\ $$ Commented…
Question Number 144342 by ArielVyny last updated on 25/Jun/21 $${Montrer}\:{que}\:\forall{n}\in\mathbb{Z} \\ $$$${E}\left(\frac{{n}−\mathrm{1}}{\mathrm{2}}\right)+{E}\left(\frac{{n}+\mathrm{2}}{\mathrm{4}}\right)+{E}\left(\frac{{n}+\mathrm{4}}{\mathrm{4}}\right)={n} \\ $$ Answered by Olaf_Thorendsen last updated on 24/Jun/21 $$\mathrm{Selon}\:\mathrm{moi},\:\mathrm{cette}\:\mathrm{formule}\:\mathrm{est}\:\mathrm{fausse}. \\ $$$$\mathrm{According}\:\mathrm{to}\:\mathrm{me},\:\mathrm{this}\:\mathrm{formula}\:\mathrm{is}\:\mathrm{false}. \\…
Question Number 78800 by Tony Lin last updated on 20/Jan/20 $${Simplify}: \\ $$$$\underset{\mathrm{3}} {\:}\sqrt{\mathrm{3}+\frac{\mathrm{10}}{\mathrm{3}}\sqrt{\frac{\mathrm{1}}{\mathrm{3}}}{i}}+\underset{\mathrm{3}} {\:}\sqrt{\mathrm{3}−\frac{\mathrm{10}}{\mathrm{3}}\sqrt{\frac{\mathrm{1}}{\mathrm{3}}}{i}} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 144318 by mathdanisur last updated on 24/Jun/21 Answered by justtry last updated on 24/Jun/21 Commented by mathdanisur last updated on 25/Jun/21 $${alot}\:{cool}\:{thanks}\:{Sir} \\…
Question Number 13154 by tawa tawa last updated on 15/May/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{number}\:\mathrm{such}\:\mathrm{that}\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{18}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{is}\:\mathrm{17}, \\ $$$$\mathrm{When}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{20}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{is}\:\mathrm{19}.\:\mathrm{and}\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{24}\:\mathrm{the}\:\mathrm{remainder}\: \\ $$$$\mathrm{is}\:\mathrm{23}.\: \\ $$ Answered by mrW1 last updated on 15/May/17 $${N}=\mathrm{18}{i}+\mathrm{17}=\mathrm{20}{j}+\mathrm{19}=\mathrm{24}{k}+\mathrm{23}…