Question Number 223210 by fantastic last updated on 17/Jul/25 $${I}\:{have}\:{a}\:{theory}.\:{this}\:{may}\:{not}\:{be}\:{true}\:{and} \\ $$$${I}\:{cannot}\:{prove}\:{it}\:.\:{I}\:{think} \\ $$$${If}\:{you}\:{want}\:{to}\:{draw} \\ $$$$\:{a}\:{closed}\:{shape}\:{in}\:{x}^{{th}} \:{dimention} \\ $$$${the}\:{minimum}\:{number}\:{of} \\ $$$$\:{vertex}\:{you}\:{will}\:{need}\:{is}\:{x}+\mathrm{1} \\ $$$$ \\ $$$$\:{like}\:{if}\:{you}\:{want}\:{to}\:{draw}\:{a}\:{closed}\:{shape}…
Question Number 223169 by wewji12 last updated on 16/Jul/25 $$\mathrm{evaluate}\: \\ $$$$\underset{{h}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{{h}−\mathrm{1}} }{{p}_{{h}} }\:\:,\:{p}_{{h}} \in\mathbb{P}\left(\mathrm{Set}\:\mathrm{of}\:\mathrm{primes}\right)\:,\:{h}\in\mathbb{Z} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 223085 by wewji12 last updated on 14/Jul/25 Answered by wewji12 last updated on 14/Jul/25 $$\mathrm{if}\:\mathrm{sequence}\:{A}_{{n}} \:\mathrm{is}\:\mathrm{monotonic}\:\mathrm{decrease}.\: \\ $$$$\bullet\:\:{A}_{{n}} \:\mathrm{satisfie}\:{A}_{\mathrm{0}} \geq{A}_{\mathrm{1}} \geq….\geq{A}_{{n}} \\ $$$$\bullet\:\:\underset{{n}\rightarrow\infty}…
Question Number 223032 by MrGaster last updated on 13/Jul/25 $$ \\ $$$$\:\:\:\:\underset{{t}=\mathrm{0}} {\overset{\mathrm{2}^{\mathrm{2024}} } {\prod}}\left(\mathrm{4sin}^{\mathrm{2}} \frac{{t}\pi}{\mathrm{2}^{\mathrm{2025}} }−\mathrm{3}\right) \\ $$ Answered by MrGaster last updated on…
Question Number 223049 by wewji12 last updated on 13/Jul/25 $$\mathrm{we}\:\mathrm{already}\:\mathrm{know}\:\:\underset{{h}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{h}}=\infty\:\mathrm{and}\:\underset{{p}\in\mathbb{P}} {\sum}\:\frac{\mathrm{1}}{{p}}=\infty \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{Harmonic}\:\mathrm{Series} \\ $$$$\underset{{h}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{h}}=\underset{{p}\in\mathbb{P}} {\prod}\:\left(\mathrm{1}+\frac{\mathrm{1}}{{p}}+\left(\frac{\mathrm{1}}{{p}}\right)^{\mathrm{2}} +\left(\frac{\mathrm{1}}{{p}}\right)^{\mathrm{3}} +…\right)=\:\underset{{p}\in\mathbb{P}} {\prod}\:\frac{\mathrm{1}}{\mathrm{1}−{p}^{−\mathrm{1}} } \\…
Question Number 223000 by MrGaster last updated on 12/Jul/25 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\frac{\mathrm{1}}{{e}}\left(\frac{{n}+\mathrm{1}}{{n}}\right)^{{n}} \right)^{\left(−\mathrm{1}\right)^{{n}} } =\frac{{e}\centerdot\sqrt{\pi}\centerdot\sqrt[{\mathrm{6}}]{\mathrm{2}}}{{A}^{\mathrm{6}} } \\ $$ Commented by MathematicalUser2357 last updated on 22/Jul/25…
Question Number 222954 by klipto last updated on 11/Jul/25 $$ \\ $$ Commented by klipto last updated on 11/Jul/25 Commented by gabthemathguy25 last updated on…
Question Number 222845 by Nicholas666 last updated on 09/Jul/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Evaluate}; \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\:\left(−\mathrm{1}\right)^{{k}} \:\begin{pmatrix}{\mathrm{2}{n}\:−\:{k}}\\{\:\:\:\:\:\:\:\:{k}}\end{pmatrix} \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 222828 by wewji12 last updated on 09/Jul/25 $$\mathrm{vector}\:\mathrm{field}\:\:\overset{\rightarrow} {\boldsymbol{\mathrm{F}}};\mathbb{R}^{\mathrm{3}} \rightarrow\mathbb{R}^{\mathrm{3}} \:,\:{F}_{{h}} \in\mathcal{C}^{\omega} \\ $$$$\mathrm{and}\:\mathrm{Let}'\mathrm{s}\:\mathrm{define}\:\mathrm{as}\:\overset{\rightarrow} {\boldsymbol{\mathrm{A}}}=\overset{\rightarrow} {\bigtriangledown}×\overset{\rightarrow} {\boldsymbol{\mathrm{F}}} \\ $$$$\mathrm{can}\:\mathrm{we}\:\mathrm{find}\:\mathrm{vector}\:\mathrm{field}\:\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}…..??? \\ $$$$\mathrm{Curl}\:\mathrm{and}\:\mathrm{Divergence}\:\:\mathrm{inverse}\:\mathrm{operator}\:\mathrm{dose}\:\mathrm{exist}?? \\…
Question Number 222711 by sonukgindia last updated on 05/Jul/25 Answered by gabthemathguy25 last updated on 05/Jul/25 $$\left({ABC}\right)_{\mathrm{16}} =\mathrm{10}×\mathrm{16}^{\mathrm{2}} +\mathrm{11}×\mathrm{16}^{\mathrm{1}} +\mathrm{12}×\mathrm{16}^{\mathrm{0}} \\ $$$$\Rightarrow\mathrm{10}×\mathrm{256}+\mathrm{11}×\mathrm{16}+\mathrm{12}=\mathrm{2560}+\mathrm{176}+\mathrm{12}=\mathrm{2748} \\ $$$$\mathrm{its}\:\mathrm{1},\:\mathrm{2748}. \\…