Question Number 138600 by Raxreedoroid last updated on 15/Apr/21 $$\mathrm{prove}\:\mathrm{or}\:\mathrm{disprove} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{f}\left({k}\right)={f}\left(\mathrm{1}\right)+\underset{{k}=\mathrm{2}} {\overset{{n}} {\sum}}\left(\frac{\underset{{i}=\mathrm{1}} {\overset{{k}−\mathrm{1}} {\sum}}\left(−\mathrm{1}\right)^{{i}+\mathrm{1}} {f}\left({i}+\mathrm{1}\right){C}_{{i}−\mathrm{1}} ^{{k}−\mathrm{2}} }{\left({k}−\mathrm{1}\right)!}\:\underset{{i}=\mathrm{1}} {\overset{{k}−\mathrm{1}} {\prod}}\left({n}−{i}\right)\right) \\ $$…
Question Number 138603 by Ar Brandon last updated on 15/Apr/21 $$\frac{\mathrm{1}}{\mathrm{2}\pi\mathrm{i}}\underset{\mathrm{T}\rightarrow\infty} {\mathrm{lim}}\underset{\gamma−\mathrm{iT}} {\overset{\gamma+\mathrm{iT}} {\int}}\frac{\mathrm{e}^{\mathrm{st}} }{\mathrm{s}−\mathrm{a}}\mathrm{ds} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 138598 by qaz last updated on 15/Apr/21 $$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}!\left(\mathrm{2}{n}+\mathrm{3}\right)}\left(\frac{\mathrm{4}}{\pi}\right)^{{n}} =? \\ $$ Answered by mr W last updated on 15/Apr/21 $${e}^{{x}}…
Question Number 73059 by mathmax by abdo last updated on 05/Nov/19 $${let}\:{P}_{{n}} \left({x}\right)=\left({x}+\mathrm{1}\right)^{{n}} −\left({x}−\mathrm{1}\right)^{{n}} \\ $$$$\left.\mathrm{1}\right)\:{fartorize}\:{inside}\:{C}\left({x}\right)\:{P}_{{n}} \left({x}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:\prod_{{k}=\mathrm{1}} ^{{p}} \:{cotan}\left(\frac{{k}\pi}{\mathrm{2}{p}+\mathrm{1}}\right) \\ $$ Commented by…
Question Number 73056 by mathmax by abdo last updated on 05/Nov/19 $${if}\:\left({xsina}+{cosa}\right)^{{n}} ={q}\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)+{r}\:{find}\:{r} \\ $$ Commented by mathmax by abdo last updated on 06/Nov/19…
Question Number 138594 by Ar Brandon last updated on 15/Apr/21 Commented by Ar Brandon last updated on 15/Apr/21 $$\mathrm{In}\:\mathrm{honour}\:\mathrm{of}\:\mathrm{Leonhard}\:\mathrm{Euler} \\ $$$$\mathrm{on}\:\mathrm{his}\:\mathrm{314}^{\mathrm{th}} \:\mathrm{anniversary}. \\ $$ Commented…
Question Number 73057 by mathmax by abdo last updated on 05/Nov/19 $${let}\:{P}_{{n}} =\left({x}+\mathrm{1}\right)^{\mathrm{2}{n}+\mathrm{1}} −{x}^{\mathrm{2}{n}+\mathrm{1}} −\mathrm{1} \\ $$$${prove}\:{that}\:{x}^{\mathrm{2}} \:+{x}\:{divide}\:\underset{{n}} {{P}} \\ $$ Answered by MJS last…
Question Number 7519 by Tawakalitu. last updated on 01/Sep/16 $${A}\:\left(\mathrm{2}\:×\:\mathrm{3}\right)\:{rectangle}\:{and}\:{a}\:\left(\mathrm{3}\:×\:\mathrm{4}\right)\:{rectangle}\:{are}\:{contain}\:{within}\: \\ $$$${a}\:{square}\:{without}\:{over}\:{laping}\:{at}\:{any}\:{inferior}\:{point}\:,\:{and}\:{the}\: \\ $$$${sides}\:{of}\:{the}\:{square}\:{are}\:{parallel}\:{to}\:{the}\:{sides}\:{of}\:{the}\:{two}\:{given} \\ $$$${rectangles}.\:{what}\:{is}\:{the}\:{smallest}\:{possible}\:{area}\:{of}\:{the}\:{square}. \\ $$ Commented by Rasheed Soomro last updated on…
Question Number 73055 by mathmax by abdo last updated on 05/Nov/19 $${decompose}\:{inside}\:{R}\left({x}\right)\:{the}\:{fraction}\:\:\frac{{x}^{\mathrm{4}} \:+{x}+\mathrm{1}}{{x}\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{3}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 73052 by mathmax by abdo last updated on 05/Nov/19 $${let}\:{P}_{{n}} ={X}^{{n}} \:+{X}^{{n}−\mathrm{1}} \:+….+{X}^{\mathrm{2}} \:+{X}−\mathrm{1}\:\in{R}\left[{X}\right] \\ $$$$\left.\mathrm{1}\left.\right){prove}\:{that}\:{P}_{{n}} {have}\:{one}\:{root}\:{x}_{{n}} \:{inside}\:\right]\mathrm{0},+\infty\left[\right. \\ $$$$\left.\mathrm{2}\right){study}\:{the}\:{sequence}\:{x}_{{n}} \\ $$ Answered…