Category: Arithmetic

Question Number 62570 by aliesam last updated on 23/Jun/19 Commented by mathmax by abdo last updated on 23/Jun/19 $${we}\:{have}\:{S}\left({x}\right)\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{sin}\left({nx}\right)}{\mathrm{2}^{{n}−\mathrm{1}} }\:=\mathrm{2}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{sin}\left({nx}\right)}{\mathrm{2}^{{n}} }\:=\mathrm{2}\:{Im}\left(\sum_{{n}=\mathrm{1}}…

Question Number 128012 by mathocean1 last updated on 03/Jan/21 $$showthat\mathrm{\forall }n\in \mathbb{N},12divise{n}^2(n^4-1)$$ Answered by MJS_new last updated on 03/Jan/21 $$n=2k\Rightarrow 2\mid n\Rightarrow 4\mid n^2$$$${n}=\mathrm{2}{k}+\mathrm{1}\:\Rightarrow\:{n}^{\mathrm{4}} −\mathrm{1}=\mathrm{8}{k}\left({k}−\mathrm{1}\right)\left(\mathrm{2}{k}^{\mathrm{2}}…

Question Number 62322 by aliesam last updated on 19/Jun/19 Commented by arcana last updated on 19/Jun/19 $${\beta }_1=\alpha +{\alpha }^6$$$$\beta_{\mathrm{2}} =\left(\alpha+\alpha^{\mathrm{6}} \right)^{\mathrm{2}} −\mathrm{2}=\alpha^{\mathrm{2}} +\mathrm{2}\alpha^{\mathrm{7}} +\alpha^{\mathrm{12}}…

Question Number 62263 by Tawa1 last updated on 18/Jun/19 Answered by behi83417@gmail.com last updated on 19/Jun/19 $$\mathrm{x}+\sqrt{\mathrm{x}-2}=\mathrm{a}\Rightarrow \frac{2}{\mathrm{a}}=\frac{1}{\mathrm{x}+\sqrt{\mathrm{x}-2}}=\frac{\mathrm{x}-\sqrt{\mathrm{x}-2}}{1}$$$$\frac{2}{\mathrm{a}}+\sqrt{\mathrm{a}}=3\Rightarrow \mathrm{a}\sqrt{\mathrm{a}}-3\mathrm{a}+2=0$$$$\sqrt{\mathrm{a}}=\mathrm{t}\Rightarrow {\mathrm{t}}^3-{3\mathrm{t}}^2+2=0$$$$\Rightarrow\left(\mathrm{t}−\mathrm{1}\right)\left(\mathrm{t}^{\mathrm{2}}…

Question Number 127504 by Snail last updated on 30/Dec/20 Terms of Service Privacy Policy Contact: info@tinkutara.com