Category: Algebra

Question Number 185337 by Shrinava last updated on 20/Jan/23 Answered by qaz last updated on 20/Jan/23 $$\underset{k=2}{\sum ^n}\frac{k+\sqrt{k}}{k}\sim {\int }_2^n\frac{x+\sqrt{x}}{x}dx\sim n$$$$\underset{{k}=\mathrm{2}} {\overset{{n}} {\sum}}\frac{{k}+\sqrt[{\mathrm{3}}]{{k}}}{{k}}\sim\int_{\mathrm{2}}…

Question Number 119801 by Ar Brandon last updated on 27/Oct/20 $$\mathrm{If}f:\mathbb{R}\to \mathbb{R}\mathrm{is}\mathrm{a}\mathrm{function}\mathrm{such}\mathrm{that}f\left(0\right)=1\mathrm{and}f(\mathrm{x}+f\left(\mathrm{y}\right))=$$$$f\left(\mathrm{x}\right)+\mathrm{y}\mathrm{for}\mathrm{all}\mathrm{x},\mathrm{y}\in \mathbb{R},\mathrm{then}$$$$\left(\mathrm{A}\right)1\mathrm{is}\mathrm{a}\mathrm{period}\mathrm{of}f$$$$\left(\mathrm{B}\right)f\left(n\right)=1\mathrm{for}\mathrm{all}\mathrm{integers}n$$$$\left(\mathrm{C}\right)f\left(n\right)=n\mathrm{for}\mathrm{all}\mathrm{integers}n$$$$\left(\mathrm{D}\right)f(-1)=0$$ Terms of…

Question Number 119797 by Ar Brandon last updated on 27/Oct/20 $$\mathrm{Q}1$$$$\mathrm{Let}{M}_2\mathrm{be}\mathrm{the}\mathrm{set}\mathrm{of}\mathrm{square}\mathrm{matrices}\mathrm{of}\mathrm{order}2\mathrm{over}$$$$\mathrm{the}\mathrm{real}\mathrm{number}\mathrm{system}\mathrm{and}$$$$\mathcal{R}=\{(A,B)\in M_2\times M_2\mid A=P^{\mathrm{T}}BP\mathrm{for}\mathrm{some}$$$$\mathrm{non}-\mathrm{singular}P\in M\}$$$$\mathrm{Then}\:\mathcal{R}\:\mathrm{is}…

Question Number 185315 by Shrinava last updated on 20/Jan/23 $$\mathrm{Solve}\mathrm{the}\mathrm{equation}:$$$$\mathrm{x}!={\mathrm{x}}^2-3\mathrm{x}+20$$ Answered by Rasheed.Sindhi last updated on 20/Jan/23 $${f}\left({x}\right)=\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{3x}\:+\:\mathrm{20}−{x}! \…

Question Number 185310 by mathlove last updated on 20/Jan/23 Commented by HeferH last updated on 20/Jan/23 $$sumadesumas?$$ Answered by Rasheed.Sindhi last updated on…