Question Number 196325 by sniper237 last updated on 22/Aug/23 $$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}{arg}\left({n}^{\mathrm{2}} +{n}+\mathrm{1}+{i}\right)=\:\pi/\mathrm{2}\: \\ $$ Answered by witcher3 last updated on 22/Aug/23 $$=\underset{\mathrm{n}\geqslant\mathrm{0}} {\sum}\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{1}+\mathrm{n}+\mathrm{n}^{\mathrm{2}}…
Question Number 196324 by sonukgindia last updated on 22/Aug/23 Answered by sniper237 last updated on 22/Aug/23 $${a}\left(\mathrm{22}\right)−{a}\left(\mathrm{21}\right)=\mathrm{3}×\mathrm{21}−\mathrm{1} \\ $$$${a}\left(\mathrm{21}\right)−{a}\left(\mathrm{20}\right)=\mathrm{3}×\mathrm{20}−\mathrm{1} \\ $$$$… \\ $$$${a}\left(\mathrm{3}\right)−{a}\left(\mathrm{2}\right)=\mathrm{3}×\mathrm{2}−\mathrm{1} \\ $$$${a}\left(\mathrm{2}\right)−{a}\left(\mathrm{1}\right)=\mathrm{3}×\mathrm{1}−\mathrm{1}…
Question Number 196327 by pticantor last updated on 22/Aug/23 $$\boldsymbol{{calcul}}\:\boldsymbol{{la}}\:\boldsymbol{{somme}}\:\boldsymbol{{suivante}}: \\ $$$$\:\:\boldsymbol{{li}}\underset{\boldsymbol{{n}}\rightarrow+\infty} {\boldsymbol{{m}}}\:\underset{\boldsymbol{{k}}=\boldsymbol{{n}}} {\overset{\mathrm{2}\boldsymbol{{n}}} {\sum}}\boldsymbol{{sin}}\left(\frac{\boldsymbol{\pi}}{\boldsymbol{{k}}}\right) \\ $$$$\:\:\boldsymbol{{elrochi}} \\ $$ Answered by sniper237 last updated on…
Question Number 196321 by sniper237 last updated on 22/Aug/23 $$\:\:\:\underset{{n}\rightarrow+\infty} {\mathrm{lim}}\:{sin}\left(\mathrm{2}\pi\sqrt{{n}^{\mathrm{2}} +\mathrm{1}\:}\:\right)\:=\:\mathrm{0} \\ $$$$\:\:\:\:\underset{{n}\rightarrow+\infty} {\mathrm{lim}}\:\:{arg}\left({n}^{\mathrm{2}} +{n}+\mathrm{1}+{i}\right)\:=\:\mathrm{0} \\ $$ Answered by witcher3 last updated on 22/Aug/23…
Question Number 196320 by sniper237 last updated on 22/Aug/23 $$\:\:{If}\:\:{a}\:\:{regular}\:{n}−{polygon}\:{can} \\ $$$$\:{be}\:{divided}\:{into}\:\:{n}\:\:{identical}\:\: \\ $$$${equilateral}\:{triangles}\:{then}\:\:{n}=\mathrm{6} \\ $$ Answered by Rasheed.Sindhi last updated on 23/Aug/23 $${n}−{polygon}\:{consists}\:{n}\:\boldsymbol{{equilateral}}\:\boldsymbol{{triangles}} \\…
Question Number 196288 by mathlove last updated on 22/Aug/23 $$\mathrm{4}^{{x}} =\sqrt{\mathrm{5}^{{y}} }=\mathrm{400} \\ $$$$\frac{{xy}}{\mathrm{2}{x}+{y}}=? \\ $$ Commented by hardmath last updated on 22/Aug/23 $$\rightarrow\:\mathrm{x}\:=\:\mathrm{log}_{\mathrm{2}} \left(\mathrm{20}\right)…
Question Number 196322 by sniper237 last updated on 22/Aug/23 $$\:\:\:\:{f}^{\left(\mathrm{1}/\mathrm{2}\right)} \left({x}\right)=\:\frac{{d}}{{dx}}\left(\int_{\mathrm{0}} ^{{x}} \:\frac{{f}\left({x}−{t}\right)}{\:\sqrt{\pi{t}}}{dt}\right) \\ $$$${Prove}\:\:{that}\:\:\:\:\left({f}^{\left(\mathrm{1}/\mathrm{2}\right)} \right)^{\left(\mathrm{1}/\mathrm{2}\right)} =\:{f}\:'\:\:\:\: \\ $$$${At}\:\:{least}\:\:{for}\:\:{f}\:=\:\:\mathrm{1}\:\:{then}\:\:{f}\:=\:{x} \\ $$ Answered by witcher3 last…
Question Number 196285 by York12 last updated on 21/Aug/23 $${problem}\:\mathrm{196258}\:\left({please}\right) \\ $$ Commented by Rasheed.Sindhi last updated on 22/Aug/23 $${Q}#\mathrm{196258}\:\left({please}\right) \\ $$ Terms of Service…
Question Number 196277 by cortano12 last updated on 21/Aug/23 $$\:\:\:\:\:\cancel{\underline{\underbrace{ }}\:} \\ $$ Answered by mr W last updated on 21/Aug/23 $${say}\:{z}=\mathrm{sin}^{\mathrm{3}} \:{x} \\ $$$$\frac{{dz}}{{dy}}=\frac{{dz}}{{dx}}×\frac{{dx}}{{dy}}=\mathrm{3}\:\mathrm{sin}^{\mathrm{2}}…
Question Number 196276 by SaRahAli last updated on 21/Aug/23 Answered by MM42 last updated on 21/Aug/23 $$\int\:\frac{{dx}}{\mathrm{1}+{sin}\mathrm{2}{x}}\:=\int\:\frac{\mathrm{1}+{tan}^{\mathrm{2}} {x}}{\left(\mathrm{1}+{tanx}\right)^{\mathrm{2}} }\:{dx} \\ $$$$\overset{\mathrm{1}+{tanx}={u}} {=}\:\int\:\frac{{du}}{{u}}\:={lnu}+{c} \\ $$$$={ln}\left(\mathrm{1}+{tanx}\right)+{c}\:\checkmark \\…