Category: Arithmetic

Question Number 124116 by danielasebhofoh last updated on 30/Nov/20 Answered by Dwaipayan Shikari last updated on 01/Dec/20 $$\int x^{-x}dx$$$$=\underset{{n}\geqslant\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} \int\frac{\left({xlogx}\right)^{{n}} }{{n}!}{dx}…

Question Number 189624 by Rupesh123 last updated on 19/Mar/23 Answered by Rasheed.Sindhi last updated on 19/Mar/23 $$x^2-(a+b)x+ab=x^2+(c-6)x-6c+5$$$$-(a+b)=c-6\wedge ab=5-6c$$$$c=-a-b+6\wedge ab=5-6(-a-b+6)$$$${ab}=\mathrm{6}{a}+\mathrm{6}{b}−\mathrm{31}…

Question Number 189563 by Rupesh123 last updated on 18/Mar/23 Answered by FelipeLz last updated on 19/Mar/23 $${V}\:=\:\left({r}_{\mathrm{1}} +\mathrm{2}\right)×\left({r}_{\mathrm{2}} +\mathrm{2}\right)×\left({r}_{\mathrm{3}} +\mathrm{2}\right)\:=\:{r}_{\mathrm{1}} {r}_{\mathrm{2}} {r}_{\mathrm{3}} +\mathrm{2}\left({r}_{\mathrm{1}} {r}_{\mathrm{2}} +{r}_{\mathrm{1}}…

Question Number 189464 by Rupesh123 last updated on 17/Mar/23 Answered by Rasheed.Sindhi last updated on 17/Mar/23 $$4a_{n+1}^2-4a_n{a}_{n+1}+a_n^2-1=0$$$${n}=\mathrm{1}:…

Question Number 123869 by benjo_mathlover last updated on 28/Nov/20 Answered by liberty last updated on 29/Nov/20 $$let:a,ar,{ar}^2,{ar}^{3}thefourconsecutivetermsinGP$$$${given}\:{the}\:{condition}\:\underset{{i}=\mathrm{1}} {\overset{\mathrm{4}} {\sum}}{u}_{{i}} \:=\:{a}+{ar}+{ar}^{\mathrm{2}} +{ar}^{\mathrm{3}}…