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n-1-x-2n-2n-1-2-pix-2-cot-pix-

Question Number 138068 by Ñï= last updated on 09/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{x}^{\mathrm{2}{n}} \zeta\left(\mathrm{2}{n}\right)=\frac{\mathrm{1}}{\mathrm{2}}−\frac{\pi{x}}{\mathrm{2}}\mathrm{cot}\:\pi{x} \\ $$ Answered by Dwaipayan Shikari last updated on 09/Apr/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty}…

We-throw-2-times-a-cubic-dice-Its-faces-are-numeroted-0-0-1-1-1-1-We-note-a-the-result-of-the-face-throw-and-b-the-result-of-second-one-1-Calculate-the-probabilities-to-have-a-and-b-which-ve

Question Number 138060 by mathocean1 last updated on 09/Apr/21 $${We}\:{throw}\:\mathrm{2}\:{times}\:{a}\:{cubic}\:{dice}\:.\:{Its} \\ $$$${faces}\:{are}\:{numeroted}\:\mathrm{0},\:\mathrm{0},\:−\mathrm{1},\:\mathrm{1},\mathrm{1},\mathrm{1}. \\ $$$${We}\:{note}\:{a}\:{the}\:{result}\:{of}\:{the}\:{face}\:{throw} \\ $$$${and}\:{b}\:{the}\:{result}\:{of}\:{second}\:{one}.\: \\ $$$$\left.\mathrm{1}\right){Calculate}\:{the}\:{probabilities}\:{to}\:{have}\: \\ $$$${a}\:{and}\:{b}\:{which}\:{verify}\:: \\ $$$$\bullet{a}=−\mathrm{1}\:{and}\:{b}=\mathrm{0} \\ $$$$\bullet{a}=\mathrm{1}\:{and}\:{b}=\mathrm{0} \\…

Find-all-continuous-functions-f-x-such-that-f-2x-1-f-x-for-all-real-x-

Question Number 6946 by 314159 last updated on 03/Aug/16 $${Find}\:{all}\:{continuous}\:{functions}\:{f}\left({x}\right)\:{such}\: \\ $$$${that}\:{f}\left(\mathrm{2}{x}+\mathrm{1}\right)={f}\left({x}\right)\:{for}\:{all}\:{real}\:{x}. \\ $$ Commented by Yozzii last updated on 04/Aug/16 $${f}\left(\mathrm{1}\right)={f}\left(\mathrm{0}\right) \\ $$$${f}'\left({x}\right)=\mathrm{2}{f}'\left(\mathrm{2}{x}+\mathrm{1}\right) \\…

Find-the-value-of-1-sin-2-1-sin-4-1-sin-8-1-sin-16-1-sin-2-1029-

Question Number 72447 by Maclaurin Stickker last updated on 28/Oct/19 $${Find}\:{the}\:{value}\:{of}: \\ $$$$\frac{\mathrm{1}}{{sin}\:\mathrm{2}°}+\frac{\mathrm{1}}{{sin}\:\mathrm{4}°}+\frac{\mathrm{1}}{{sin}\:\mathrm{8}°}+\frac{\mathrm{1}}{{sin}\:\mathrm{16}°}+… \\ $$$$+\frac{\mathrm{1}}{{sin}\:\left(\mathrm{2}^{\mathrm{1029}} \right)^{°} } \\ $$ Answered by Tanmay chaudhury last updated…

Question-72439

Question Number 72439 by Maclaurin Stickker last updated on 28/Oct/19 Commented by Maclaurin Stickker last updated on 28/Oct/19 $${Prove}\:{that}\:{the}\:{radius}\:{of}\:{the}\: \\ $$$${circumferences}\:{is}: \\ $$$$\frac{\mathrm{2}}{\mathrm{1}−{cos}\:\mathrm{2}\alpha}\:{and}\:\frac{\mathrm{2}}{\mathrm{1}−{sin}\:\mathrm{2}\alpha}\:. \\ $$$${and}\:{find}\:{tan}\left(\alpha\right)…