Category: Algebra

Question Number 99846 by bachamohamed last updated on 23/Jun/20 $$\mathit{l}\mathit{i}\underset{\mathit{n}\to \mathrm{\infty }}{\mathit{m}}{(1-\frac{1}{2!})}^{{(\frac{1}{2!}-\frac{1}{3!})}^{\dots \dots \dots (\frac{1}{\mathit{n}!}-\frac{1}{(\mathit{n}+1)!})}}=?$$ Commented by Dwaipayan Shikari last updated on 23/Jun/20 $${Ans}=\mathrm{1} \…

Question Number 34305 by abdo mathsup 649 cc last updated on 03/May/18 $$let]A=\left(\begin{array}{c}110\\ 111\end{array}\right)$$$$(011$$$$1)findthecaractetisticpolynomofA$$$$2)calculate{A}^n$$ Commented by prof Abdo…

Question Number 165364 by mathlove last updated on 31/Jan/22 Answered by Ar Brandon last updated on 31/Jan/22 $$S=\frac{1}{1+e^{-99}}+\frac{1}{1+e^{-98}}+\cdot \cdot \cdot +\frac{1}{1+e^{98}}+\frac{1}{1+e^{99}}$$$$\:\:\:\:=\frac{{e}^{\mathrm{99}} }{\mathrm{1}+{e}^{\mathrm{99}}…

Question Number 165362 by HongKing last updated on 31/Jan/22 Answered by aleks041103 last updated on 01/Feb/22 $$ifgcd(a,b)=1andb>a,then:$$$$for\mathrm{\forall }r=0,1,2,\dots ,b-1,\mathrm{\exists }k\in \mathbb{N}suchthat$$$$ka\equiv r\left(modb\right).$$$$$$$${In}\:{our}\:{case},\:{gcd}\left(\mathrm{19},\mathrm{360}\right)=\mathrm{1}…

Question Number 99807 by PengagumRahasiamu last updated on 23/Jun/20 Answered by ajfour last updated on 23/Jun/20 $$x=54,y=24,z=6$$$$x+y+z=84.$$$$$$ Commented by…