Category: Arithmetic

Question Number 4639 by FilupSmith last updated on 17/Feb/16 $$\mathrm{Is}\mathrm{the}\mathrm{section}\mathrm{marked}(\ast )correct?$$$$$$$$\underset{i=1}{\prod ^x}i=x!$$$$$$$$\underset{{n}=\mathrm{1}} {\overset{{x}} {\prod}}\left(\underset{{i}=\mathrm{1}} {\overset{{n}} {\prod}}{i}\right)=\mathrm{1}!×\mathrm{2}!×…×{x}! \…

Question Number 135642 by Raxreedoroid last updated on 14/Mar/21 $$\mathrm{Write}\underset{k=0}{\sum ^{n-2}}{3}^k\mathrm{in}\mathrm{terms}\mathrm{of}n.\mathrm{Where}n\in \mathbb{N}.$$ Answered by Ñï= last updated on 14/Mar/21 $$\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{2}} {\sum}}\mathrm{3}^{{k}}…

Question Number 135609 by physicstutes last updated on 14/Mar/21 $$\mathrm{express}\mathrm{the}\mathrm{number}\frac{3}{13}\mathrm{as}\mathrm{a}\mathrm{decimal}\mathrm{ane}\mathrm{state}\mathrm{the}$$$$\mathrm{value}\mathrm{of}\mathrm{the}{300}^{\mathrm{th}}\mathrm{value}$$ Answered by Olaf last updated on 14/Mar/21 $$\frac{\mathrm{3}}{\mathrm{13}}\:=\:\mathrm{0},\overline {\mathrm{230769}} \…

Question Number 4454 by FilupSmith last updated on 29/Jan/16 $$S=\frac{x-1}{x+1}+\frac{x-2}{x^2-2}+\frac{x-3}{x^3+3}+\frac{x-4}{x^4-4}+\dots$$$$$$$$S=\underset{i=1}{\sum ^{\mathrm{\infty }}}\frac{x-i}{x^i-{(-1)}^{i}i}$$$$D\mathrm{oes}\mathrm{S}limitt\mathrm{o}\mathrm{a}\mathrm{value}\mathrm{for}\pm x?$$…

Question Number 4285 by Filup last updated on 07/Jan/16 $$S=1+\sqrt{2+\sqrt{3+\sqrt{4+\dots }}}$$$$S=???$$ Commented by RasheedSindhi last updated on 07/Jan/16 $$\mathrm{S}=\sqrt{2+\sqrt{3+\sqrt{4+\dots }}}$$$${S}\left({n}\right)=\sqrt{\left({n}+\mathrm{1}\right)+{S}\left({n}+\mathrm{1}\right)} \…