Question Number 45356 by MrW3 last updated on 12/Oct/18 $${x}=\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{1}}{\mathrm{3}+\frac{\mathrm{1}}{\mathrm{4}+…}}}}=? \\ $$ Answered by MJS last updated on 12/Oct/18 $$\mathrm{non}−\mathrm{periodic}\:\mathrm{infinite}\:\mathrm{continued}\:\mathrm{fractions} \\ $$$$\mathrm{are}\:\mathrm{transcendental}\:\mathrm{numbers},\:\mathrm{at}\:\mathrm{least}\:\mathrm{I}\:\mathrm{seem} \\ $$$$\mathrm{to}\:\mathrm{remember}\:\mathrm{this}.\:\mathrm{we}\:\mathrm{can}\:\mathrm{only}\:\mathrm{approximate} \\…
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Question Number 110887 by I want to learn more last updated on 31/Aug/20 Commented by Aina Samuel Temidayo last updated on 31/Aug/20 $$\exists\:\mathrm{100a}+\mathrm{10b}+\mathrm{c}\:\in\:\left(\mathrm{100},\mathrm{999}\right)\:\mathrm{s}.\mathrm{t}. \\ $$$$\mathrm{100a}+\mathrm{10b}+\mathrm{c}\:=\:\mathrm{a}^{\mathrm{3}}…
Question Number 45346 by Tawa1 last updated on 12/Oct/18 Commented by Meritguide1234 last updated on 12/Oct/18 $${this}\:{is}\:{my}\:{old}\:{post}\:\mathrm{45204} \\ $$ Commented by Tawa1 last updated on…
Question Number 176423 by Shrinava last updated on 18/Sep/22 Answered by a.lgnaoui last updated on 21/Sep/22 $$\:\frac{\mathrm{3}\pi}{{x}}=\left(\:\frac{\mathrm{4}\pi}{{x}}−\frac{\pi}{{x}}\right);\:\:\:\frac{\mathrm{5}\pi}{{x}}=\left(\frac{\mathrm{4}\pi}{{x}}+\frac{\pi}{{x}}\right);\:\:\frac{\mathrm{4}\pi}{{x}}=\mathrm{2}\left(\frac{\mathrm{2}\pi}{{x}}\right)\:\:\: \\ $$$$\mathrm{cos}\:\frac{\mathrm{3}\pi}{{x}}+\mathrm{cos}\:\frac{\mathrm{5}\pi}{{x}}=\mathrm{cos}\left(\:\frac{\mathrm{4}\pi}{{x}}−\frac{\pi}{{x}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{4}\pi}{{x}}+\frac{\pi}{{x}}\right)=\mathrm{2cos}\:\frac{\pi}{{x}}\mathrm{cos}\:\frac{\mathrm{4}\pi}{{x}} \\ $$$$ \\ $$$$\mathrm{cos}\:\frac{\pi}{{x}}+\mathrm{2cos}\:\frac{\pi}{{x}}\mathrm{cos}\:\frac{\mathrm{4}\pi}{{x}}=\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{cos}\:\frac{\mathrm{2}\pi}{{x}}+\mathrm{cos}\:\frac{\mathrm{4}\pi}{{x}} \\ $$$$\mathrm{cos}\:\frac{\pi}{{x}}\left(\mathrm{1}+\mathrm{2cos}\:\frac{\mathrm{4}\pi}{{x}}\right)=\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{cos}\:\frac{\mathrm{4}\pi}{{x}}+\mathrm{cos}\:\frac{\mathrm{2}\pi}{{x}}…
Question Number 110879 by Khanacademy last updated on 31/Aug/20 Commented by Khanacademy last updated on 31/Aug/20 $$\boldsymbol{{PLEASE}} \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 45327 by Necxx last updated on 12/Oct/18 Answered by rahul 19 last updated on 12/Oct/18 $${x}=\:\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}+\frac{\mathrm{1}}{\mathrm{1}+{x}}} \\ $$$$\Rightarrow{x}=\mathrm{1}+\frac{\mathrm{1}+{x}}{\mathrm{4}+\mathrm{3}{x}} \\ $$$$\Rightarrow\mathrm{4}{x}+\mathrm{3}{x}^{\mathrm{2}} =\mathrm{5}+\mathrm{4}{x} \\ $$$$\Rightarrow{x}=\:\underset{−}…
Question Number 176393 by BaliramKumar last updated on 18/Sep/22 $${show}\:{that} \\ $$$$\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+…………….\:\infty\:=\:\frac{−\mathrm{1}}{\mathrm{8}} \\ $$ Answered by BaliramKumar last updated on 19/Sep/22 $$\mathrm{S}\:=\:\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+\mathrm{5}+\mathrm{6}+\mathrm{7}+\mathrm{8}+\mathrm{9}+\mathrm{10}+……..\infty \\ $$$$\mathrm{S}\:=\:\mathrm{1}+\underset{\mathrm{9}} {\underbrace{\mathrm{2}+\mathrm{3}+\mathrm{4}}}+\underset{\mathrm{18}}…
Question Number 176391 by cortano1 last updated on 18/Sep/22 Commented by mr W last updated on 18/Sep/22 $${f}\left({x}\right)={x}^{\mathrm{3}} \\ $$ Answered by TheHoneyCat last updated…
Question Number 176384 by Ari last updated on 17/Sep/22 $${Find}\:{the}\:{constant}\:{term}\:{in}\:{the} \\ $$$${expansion}\:{of}\:{the}\:{expression} \\ $$$$\left(\mathrm{2}+\mathrm{3}{x}\right)^{\mathrm{3}} \left(\frac{\mathrm{1}}{{x}}−\mathrm{4}\right)^{\mathrm{4}} \\ $$ Answered by mr W last updated on 17/Sep/22…