Category: Algebra

Question Number 205726 by hardmath last updated on 28/Mar/24 $$$$101 is chosen arbitrarily from the numbers 1,2,3,…,199,200. Prove that two of these selected…

Question Number 205680 by mnjuly1970 last updated on 27/Mar/24 $$$$$$solve$$$$$$$$\lfloor x\rfloor +\lfloor x^2\rfloor =\lfloor x^3\rfloor$$$$$$ Answered by Frix…

Question Number 205672 by hardmath last updated on 26/Mar/24 Answered by Berbere last updated on 27/Mar/24 $$\mathrm{\Omega }=\underset{n\to \mathrm{\infty }}{\lim }\frac{1}{n}\underset{k=2}{\sum ^n}\frac{\sqrt{k(k-1)}}{\sqrt{{(\sqrt{k-1}+\sqrt{k})}^2}}.{\left(\underset{k=1}{\sum ^n}\sqrt{k}\right)}^{-1}$$$${S}_{\mathrm{1}}…

Question Number 205640 by hardmath last updated on 26/Mar/24 $$\mathrm{If}\mathrm{a},\mathrm{b},\mathrm{c}>0\mathrm{and}\mathrm{abc}⩾1$$$$\mathrm{Prove}\mathrm{that}:$$$$\mathrm{a}+\mathrm{b}+\mathrm{c}⩾\frac{1+\mathrm{a}}{1+\mathrm{b}}+\frac{1+\mathrm{b}}{1+\mathrm{c}}+\frac{1+\mathrm{c}}{1+\mathrm{a}}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 205671 by hardmath last updated on 26/Mar/24 Answered by Berbere last updated on 27/Mar/24 $$\left(\mathrm{1}−{x}\right)^{{n}} =\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{k}} {x}^{{k}} $$\left(\begin{array}{c}n\\ k\end{array}\right)$$\Rightarrow\int_{\mathrm{0}} ^{{t}} \underset{{k}=\mathrm{0}} {\overset{{n}}…