Question Number 11633 by Joel576 last updated on 29/Mar/17 $$\mathrm{A}\:\mathrm{geometric}\:\mathrm{sequence}\:\mathrm{with}\:{n}\:\mathrm{terms}\: \\ $$$${a}_{\mathrm{1}} ,\:{a}_{\mathrm{2}} ,\:{a}_{\mathrm{3}} ,\:…,\:{a}_{{n}} \:\mathrm{which}\:\mathrm{has}\:{a}_{\mathrm{1}} \:.\:{a}_{{n}} \:=\:\mathrm{3} \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{all}\:{n}\:\mathrm{terms}\:=\:{a}_{\mathrm{1}} {a}_{\mathrm{2}} {a}_{\mathrm{3}} …{a}_{{n}} =\:\mathrm{59049} \\…
Question Number 142698 by Willson last updated on 04/Jun/21 $$\mathrm{Prove}\:\mathrm{that}\:\forall\mathrm{n}\in\mathbb{N}^{\ast} \\ $$$$\:\:\:\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}−\mathrm{1}} {\prod}}\mathrm{sin}\left(\frac{\mathrm{k}\pi}{\mathrm{2n}}\right)\:=\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}−\mathrm{1}} {\prod}}\mathrm{cos}\left(\frac{\mathrm{k}\pi}{\mathrm{2n}}\right) \\ $$ Answered by Ar Brandon last updated on…
Question Number 11611 by Nayon last updated on 29/Mar/17 $${Can}\:{you}\:{prove}\:{the}\:{Taylor}'{s}\:{series}\: \\ $$$${without}\:{using}\:{mean}\:{value}\:{theorem}? \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 142681 by mnjuly1970 last updated on 03/Jun/21 $$ \\ $$$$\:\:\:\:{prove}\:\:{that}\::: \\ $$$$\:\:\:\:\:\:\boldsymbol{\phi}:=\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\left(\mathrm{1}+{cos}\left({x}\right)\right)}{\mathrm{1}+{e}^{\:{x}} }{dx}=\mathrm{0} \\ $$$$\:\:\:\:\:……………. \\ $$$$ \\ $$ Commented by…
Question Number 11581 by Nayon last updated on 28/Mar/17 $${cAn}\:{you}\:{prove}\:{the}\:{chAin}\:{role}?? \\ $$ Answered by linkelly0615 last updated on 28/Mar/17 $${yes}\sim \\ $$ Commented by linkelly0615…
Question Number 142655 by mnjuly1970 last updated on 03/Jun/21 $$\:\:{evaluate}….. \\ $$$$\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{{n}.{cos}\left({n}\pi\right)}{\Gamma\:\left(\mathrm{2}{n}+\mathrm{2}\right)}\right)=?\:….. \\ $$$$\:\:\:……. \\ $$ Answered by qaz last updated on 03/Jun/21…
Question Number 11580 by Nayon last updated on 28/Mar/17 $${why}\:\frac{{dy}}{{dx}}=\frac{{dy}}{{du}}.\frac{{du}}{{dx}} \\ $$ Answered by mrW1 last updated on 28/Mar/17 $${the}\:{chain}\:{rule}\:{is}\:{one}\:{of}\:{the}\:{elementary} \\ $$$${rules}.\:{you}\:{should}\:{know}\:{them},\:{but}\:\: \\ $$$${you}\:{don}'{t}\:{need}\:{to}\:{prove}\:{them}.\:{if} \\…
Question Number 11571 by Nayon last updated on 28/Mar/17 $${why}\:\:\:\frac{{d}\left[{f}\left\{{g}\left({x}\right)\right\}\right]}{{dx}}=\frac{{df}\left[\left\{{g}\left({x}\right)\right\}\right]}{{dg}\left({x}\right)}.\frac{{dg}\left({x}\right)}{{dx}}? \\ $$ Answered by mrW1 last updated on 28/Mar/17 $${y}={f}\left({u}\right) \\ $$$${u}={g}\left({x}\right) \\ $$$$\frac{{dy}}{{dx}}=\frac{{dy}}{{du}}×\frac{{du}}{{dx}} \\…
Question Number 11567 by Nayon last updated on 28/Mar/17 $${why}\:\:\:\:\:\:{li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\:\frac{{f}\left({x}\right)}{{g}\left({x}\right)}={li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\frac{{f}'\left({x}\right)}{{g}'\left({x}\right)} \\ $$ Answered by mrW1 last updated on 28/Mar/17 $${l}'{hopital}'{s}\:{rule} \\ $$ Terms…
Question Number 11565 by Nayon last updated on 28/Mar/17 $${if}\:\frac{{dy}}{{dx}}={p}\:\:,{then}\:{why}\:{dy}={pdx}? \\ $$ Answered by mrW1 last updated on 28/Mar/17 $${if}\:\frac{{dy}}{{dx}}={p}\Rightarrow{y}={px} \\ $$$$\Rightarrow{dy}={pdx} \\ $$ Terms…