Question Number 135642 by Raxreedoroid last updated on 14/Mar/21 $$\mathrm{Write}\:\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{2}} {\sum}}\mathrm{3}^{{k}} \:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:{n}.\:\mathrm{Where}\:{n}\in\mathbb{N}. \\ $$ Answered by Ñï= last updated on 14/Mar/21 $$\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{2}} {\sum}}\mathrm{3}^{{k}}…
Question Number 4555 by FilupSmith last updated on 07/Feb/16 $${y}={x}^{{i}} \\ $$$${x}\in\mathbb{R} \\ $$$${i}^{\mathrm{2}} =−\mathrm{1} \\ $$$$ \\ $$$$\mathrm{is}\:{y}\in\mathbb{C}? \\ $$ Commented by Yozzii last…
Question Number 135609 by physicstutes last updated on 14/Mar/21 $$\mathrm{express}\:\mathrm{the}\:\mathrm{number}\:\frac{\mathrm{3}}{\mathrm{13}}\:\mathrm{as}\:\mathrm{a}\:\mathrm{decimal}\:\mathrm{ane}\:\mathrm{state}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{300}^{\mathrm{th}} \:\mathrm{value} \\ $$ Answered by Olaf last updated on 14/Mar/21 $$\frac{\mathrm{3}}{\mathrm{13}}\:=\:\mathrm{0},\overline {\mathrm{230769}} \\…
Question Number 135537 by metamorfose last updated on 13/Mar/21 $${x}\:{and}\:{n}\:{are}\:{integers} \\ $$$${p}\:{is}\:{a}\:{prime}\:{number} \\ $$$${find}\:\left({x},{p},{n}\right)\:{so}\:{that}\::\:{x}^{\mathrm{2020}} +\mathrm{3}={p}^{{n}} \\ $$ Answered by Olaf last updated on 14/Mar/21 $$\mathrm{If}\:{x}\:=\:\mathrm{0},\:{p}\:=\:\mathrm{3}\:\mathrm{and}\:{n}\:=\:\mathrm{1}…
Question Number 4454 by FilupSmith last updated on 29/Jan/16 $${S}=\frac{{x}−\mathrm{1}}{{x}+\mathrm{1}}+\frac{{x}−\mathrm{2}}{{x}^{\mathrm{2}} −\mathrm{2}}+\frac{{x}−\mathrm{3}}{{x}^{\mathrm{3}} +\mathrm{3}}+\frac{{x}−\mathrm{4}}{{x}^{\mathrm{4}} −\mathrm{4}}+… \\ $$$$ \\ $$$${S}=\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{x}−{i}}{{x}^{{i}} −\left(−\mathrm{1}\right)^{{i}} {i}} \\ $$$${D}\mathrm{oes}\:\mathrm{S}\:{limit}\:{t}\mathrm{o}\:\mathrm{a}\:\mathrm{value}\:\mathrm{for}\:\pm{x}? \\ $$…
Question Number 4365 by Filup last updated on 13/Jan/16 $$\mathrm{Is}\:\mathrm{the}\:\mathrm{following}\:\mathrm{correct}? \\ $$$$ \\ $$$${S}=\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{2}^{{i}−\mathrm{1}} \\ $$$${S}=\mathrm{1}+\mathrm{2}+\mathrm{4}+\mathrm{8}+\mathrm{16}+\mathrm{32}+\mathrm{64}+\mathrm{128}+… \\ $$$$\therefore\mathrm{2}{S}=\mathrm{2}+\mathrm{4}+\mathrm{8}+\mathrm{6}+\mathrm{32}+… \\ $$$$\mathrm{2}{S}={S}−\mathrm{1} \\ $$$${S}=−\mathrm{1} \\…
Question Number 4285 by Filup last updated on 07/Jan/16 $${S}=\mathrm{1}+\sqrt{\mathrm{2}+\sqrt{\mathrm{3}+\sqrt{\mathrm{4}+…}}} \\ $$$${S}=??? \\ $$ Commented by RasheedSindhi last updated on 07/Jan/16 $$\mathrm{S}=\sqrt{\mathrm{2}+\sqrt{\mathrm{3}+\sqrt{\mathrm{4}+…}}} \\ $$$${S}\left({n}\right)=\sqrt{\left({n}+\mathrm{1}\right)+{S}\left({n}+\mathrm{1}\right)} \\…
Question Number 4092 by Filup last updated on 28/Dec/15 $$\mathrm{Prove}: \\ $$$$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{n}!}{\left({n}−{k}\right)!\:{k}!}=\mathrm{2}^{{n}} −\mathrm{1} \\ $$ Answered by Yozzii last updated on 28/Dec/15 $${According}\:{to}\:{the}\:{Binomial}\:{Theorem},…
Question Number 4066 by Filup last updated on 27/Dec/15 $$\mathrm{Can}\:\mathrm{we}\:\mathrm{prove}\:\pi\:\mathrm{is}\:\mathrm{tracendental}? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 69557 by aliesam last updated on 24/Sep/19 Answered by MJS last updated on 24/Sep/19 $${x}=\mathrm{72} \\ $$ Terms of Service Privacy Policy Contact:…