Question Number 86113 by Tony Lin last updated on 27/Mar/20 $$\left(\mathrm{1}\right){Determine}\:{the}\:{following} \\ $$$${if}\:{it}\:{is}\:{convergent}\:{or}\:{divergent} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{sin}\left({n}\right)}{{n}} \\ $$$$\left(\mathrm{2}\right)\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{sin}\left({n}^{{p}} \right)}{{n}^{{p}} },\:{p}\epsilon\mathbb{R},{find}\:{the}\:{range}\: \\ $$$${of}\:{p}\:{when}\:{it}\:{is}\:{convergent}…
Question Number 20576 by gopikrishnan005@gmail.com last updated on 28/Aug/17 $${sec}\left({A}−\mathrm{3}\Pi/\mathrm{2}\right) \\ $$ Answered by Tinkutara last updated on 28/Aug/17 $$\mathrm{sec}\:\left(\frac{\mathrm{3}\pi}{\mathrm{2}}−{A}\right)=−\mathrm{cosec}\:{A} \\ $$ Terms of Service…
Question Number 86111 by john santu last updated on 27/Mar/20 $$\mathrm{sin}\:\left(\frac{\mathrm{3}\pi}{\mathrm{2}}\mathrm{cos}\:{x}\right)\:=\:−\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Commented by jagoll last updated on 27/Mar/20 $$\Leftrightarrow\mathrm{sin}\:\left(\frac{\mathrm{3}\pi}{\mathrm{2}}\mathrm{cos}\:\mathrm{x}\right)\:=\:\mathrm{sin}\:\left(−\frac{\pi}{\mathrm{6}}\right) \\ $$$$\frac{\mathrm{3}\pi}{\mathrm{2}}\mathrm{cos}\:\mathrm{x}\:=\:−\frac{\pi}{\mathrm{6}}\:+\:\mathrm{2k}\pi \\ $$$$\mathrm{cos}\:\mathrm{x}\:=\:\frac{\mathrm{2}}{\mathrm{3}\pi}\:\left\{−\frac{\pi}{\mathrm{6}}+\mathrm{2k}\pi\right\}…
Question Number 20574 by khamizan833@gmail.com last updated on 28/Aug/17 $$\left(\mathrm{1}\:+\:\mathrm{tan}\:\mathrm{1}°\right)\left(\mathrm{1}\:+\:\mathrm{tan}\:\mathrm{2}°\right)…\left(\mathrm{1}\:+\:\mathrm{tan}\:\mathrm{45}°\right)\:=\:\mathrm{2}^{{n}+\mathrm{1}} \\ $$$$\mathrm{find}\:{n}\:! \\ $$ Answered by Tinkutara last updated on 28/Aug/17 $$\left(\mathrm{1}+\mathrm{tan}\:\mathrm{1}°\right)\left(\mathrm{1}+\mathrm{tan}\:\mathrm{44}°\right)=\mathrm{1}+\mathrm{tan}\:\mathrm{44}°+ \\ $$$$\mathrm{tan}\:\mathrm{1}°+\mathrm{tan}\:\mathrm{1}°\mathrm{tan}\:\mathrm{44}° \\…
Question Number 151641 by Tawa11 last updated on 22/Aug/21 Answered by Kamel last updated on 22/Aug/21 $${S}_{{n}} =\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\sum}}\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\mathrm{3}{k}} {dx}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}−{x}^{\mathrm{3}{n}}…
Question Number 151636 by Tawa11 last updated on 22/Aug/21 Commented by mr W last updated on 22/Aug/21 $${do}\:{you}\:{know}\:{the}\:{psi}−{function}\:{and} \\ $$$$\psi\left(\mathrm{1}+{z}\right)=−\gamma+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{{n}}−\frac{\mathrm{1}}{{n}+{z}}\right)\:? \\ $$$${if}\:{not},\:{then}\:{you}\:{should}\:{learn}\:{this}\:{at} \\…
Question Number 151638 by mathdanisur last updated on 22/Aug/21 $$\underset{\:\mathrm{0}} {\overset{\:\mathrm{2}\boldsymbol{\pi}} {\int}}\left(\mathrm{1}\:-\:\mathrm{cos}\boldsymbol{\mathrm{x}}\right)^{\mathrm{10}} \:\mathrm{cos}\left(\mathrm{10x}\right)\:\mathrm{dx}\:=\:? \\ $$ Answered by Olaf_Thorendsen last updated on 22/Aug/21 $$\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \left(\mathrm{1}−\mathrm{cos}{x}\right)^{\mathrm{10}}…
Question Number 20561 by mondodotto@gmail.com last updated on 28/Aug/17 Answered by mind is power last updated on 07/Nov/19 $$\mathrm{ln}\left(\frac{\mathrm{x}+\mathrm{1}}{\mathrm{x}−\mathrm{1}}\right)=\mathrm{ln}\left(\frac{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}}}{\mathrm{1}−\frac{\mathrm{1}\:}{\mathrm{x}}}\right) \\ $$$$\mathrm{ln}\left(\mathrm{1}+\mathrm{t}\right)=\underset{\mathrm{n}\geqslant\mathrm{1}} {\sum}\left(−\mathrm{1}\right)^{\mathrm{n}−\mathrm{1}} .\frac{\mathrm{t}^{\mathrm{n}} }{\mathrm{n}}\:\:\mathrm{if}\:\mid\mathrm{t}\mid<\mathrm{1} \\…
Question Number 86094 by M±th+et£s last updated on 27/Mar/20 $$\mathrm{2}\int\sqrt{{x}^{\mathrm{3}} +\mathrm{4}}\:{dx} \\ $$ Commented by redmiiuser last updated on 27/Mar/20 $${sir}\:{please}\:{check}\:{my}\: \\ $$$${answer} \\ $$…
Question Number 20559 by khamizan833@gmail.com last updated on 28/Aug/17 Answered by Tinkutara last updated on 28/Aug/17 $${Squaring}\:{and}\:{adding}\:{the}\:{two}\:{equations}, \\ $$$$\mathrm{9}+\mathrm{16}+\mathrm{24}\left(\mathrm{sin}\:{A}\mathrm{cos}\:{B}+\mathrm{cos}\:{A}\mathrm{sin}\:{B}\right)=\mathrm{1} \\ $$$$\mathrm{24sin}\:\left({A}+{B}\right)=−\mathrm{24} \\ $$$$\mathrm{sin}\:{C}=−\mathrm{1}\Rightarrow{This}\:{condition}\:{is}\:{not} \\ $$$${possible}.\:{Some}\:{error}\:{in}\:{the}\:{question}.…