Question Number 146072 by savitar last updated on 10/Jul/21 $${Let}\:{F}_{{n}} =\mathrm{2}^{\mathrm{2}^{{n}} } +\mathrm{1}\:{the}\:{fermat}\:{number} \\ $$$${Prove}\:{that} \\ $$$$\:{F}_{{n}} \:{is}\:{prime}\:\Leftrightarrow\:\mathrm{3}^{\frac{{F}_{{n}} −\mathrm{1}}{\mathrm{2}}} \equiv\mathrm{1}\left[{F}_{{n}} \right] \\ $$ Terms of…
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Question Number 146041 by alcohol last updated on 10/Jul/21 $${z}'\:=\:\mathrm{2}{iz}\:+\:\left(\mathrm{3}−\mathrm{3}{i}\right) \\ $$$${geometrical}\:{representation}\:{is}? \\ $$ Answered by ajfour last updated on 10/Jul/21 $$\frac{{dx}}{{dt}}+{i}\frac{{dy}}{{dt}}=\mathrm{2}{i}\left({x}+{iy}\right)+\mathrm{3}\left(\mathrm{1}−{i}\right) \\ $$$$\Rightarrow\:\frac{{dx}}{{dt}}=\mathrm{3}−\mathrm{2}{y} \\…
Question Number 145960 by puissant last updated on 10/Jul/21 Answered by mathmax by abdo last updated on 10/Jul/21 $$\mathrm{R}_{\mathrm{n}} =\sum_{\mathrm{p}=\mathrm{n}+\mathrm{1}} ^{\mathrm{2n}} \mathrm{sin}\left(\frac{\mathrm{1}}{\mathrm{p}}\right)\:\Rightarrow\mathrm{R}_{\mathrm{n}} =_{\mathrm{p}−\mathrm{n}=\mathrm{k}} \:\:\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}}…
Question Number 145940 by Mathspace last updated on 09/Jul/21 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{−{x}} {log}\left(\mathrm{1}−{x}^{\mathrm{4}} \right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 145941 by Mathspace last updated on 09/Jul/21 $${find}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\mathrm{3}{x}} {log}\left(\mathrm{1}+{x}^{\mathrm{3}} \right){dx} \\ $$ Answered by ArielVyny last updated on 24/Jul/21 $$\frac{\mathrm{3}{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{3}}…
Question Number 145936 by Mathspace last updated on 09/Jul/21 $${g}\left({x}\right)={arctan}\left({cosx}\right) \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 145938 by Mathspace last updated on 09/Jul/21 $${g}\left({x}\right)={cos}\left({arctanx}\right) \\ $$$${if}\:{g}\left({x}\right)=\Sigma\:{a}_{{n}} {x}^{{n}} \:{determine}\:{the} \\ $$$${sequence}\:{a}_{{n}} \\ $$ Answered by Olaf_Thorendsen last updated on 09/Jul/21…
Question Number 145939 by Mathspace last updated on 09/Jul/21 $$\Psi\left({x}\right)={ch}\left({sinx}\right) \\ $$$${developp}\:\Psi\:{at}\:{fourier}\:{serie} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 145809 by puissant last updated on 08/Jul/21 $$\mathrm{prove}\:\mathrm{1}+\mathrm{2}+\mathrm{3}+…..=−\frac{\mathrm{1}}{\mathrm{12}} \\ $$ Answered by Olaf_Thorendsen last updated on 09/Jul/21 $$\mathrm{A}\:=\:\mathrm{1}−\mathrm{1}+\mathrm{1}−\mathrm{1}+\mathrm{1}−… \\ $$$$\mathrm{A}\:=\:\mathrm{1}−\left(\mathrm{1}−\mathrm{1}+\mathrm{1}−\mathrm{1}+\mathrm{1}−…\right) \\ $$$$\mathrm{A}\:=\:\mathrm{1}−\mathrm{A} \\…