Category: Algebra

Question Number 32788 by rahul 19 last updated on 02/Apr/18 $$\mathit{T}heleastpositiveintegralvalueof$$$${}^{\prime }{x}^{\prime }satisfying:$$$$(e^x-2)\left(\sin (x+\frac{\pi }{4})\right)(x-{\log }_e\underset{}{2})(sinx-cosx)<0$$ Commented by rahul 19 last…

Question Number 163849 by alephzero last updated on 11/Jan/22 $$\frac{1}{1\cdot 2}+\frac{1}{2\cdot 3}+\dots \frac{1}{19\cdot 20}+\frac{1}{20\cdot 21}=?$$ Answered by cortano1 last updated on 11/Jan/22 $$\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{20}} {\sum}}\:\frac{\mathrm{1}}{{k}\left({k}+\mathrm{1}\right)}\:=\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{20}} {\sum}}\:\left(\frac{\mathrm{1}}{{k}}−\frac{\mathrm{1}}{{k}+\mathrm{1}}\right) \…

Question Number 163845 by mnjuly1970 last updated on 12/Jan/22 $$$$$$a,b\in \mathbb{N},gcd(a,b)=1$$$$provethat$$$$$$$$a^{\phi \left(b\right)}+b^{\phi \left(a\right)}\stackrel{ab}{\equiv }1$$$$\phi :\mathcal{E}ulerphifunction\dots$$$$…

Question Number 163843 by HongKing last updated on 11/Jan/22 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 32768 by Rasheed.Sindhi last updated on 01/Apr/18 $$\mathrm{Prove}\mathrm{that}{a}^2+b^2+c^2⩾ab+bc+ca$$$$\mathrm{\forall }a,b,c\in \mathbb{R}$$ Answered by mrW2 last updated on 02/Apr/18 $${a}^{\mathrm{2}}…