Category: Arithmetic

Question Number 41721 by Rio Michael last updated on 11/Aug/18 $${show}\:{that} \\ $$$${U}_{{n}} =\:\mathrm{1}+\:{nx}\:+\:\frac{{n}\left({n}−\mathrm{1}\right)}{\mathrm{2}!}\:{x}^{\mathrm{2}\:\:} +\:\frac{{n}\left({n}−\mathrm{1}\right)\left({n}−\mathrm{2}\right)}{\mathrm{3}!}{x}^{\mathrm{3}} +\:…. \\ $$$${for}\:{which}\:{U}_{{n}} =\:\left(\mathrm{1}\:+\:{x}\right)^{{n}} . \\ $$ Commented by maxmathsup…

Question Number 172632 by Mikenice last updated on 29/Jun/22 Commented by peter frank last updated on 29/Jun/22 $$\mathrm{thank}\:\mathrm{you} \\ $$ Commented by mr W last…

Question Number 106880 by bemath last updated on 07/Aug/20 $$\:\:\:\:\:\:\:\:\:\:\overset{@\mathrm{bemath}@} {\:} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{m}\:\mathrm{so}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{x}^{\mathrm{4}} \:−\left(\mathrm{m}+\mathrm{2}\right)\mathrm{x}^{\mathrm{2}} +\mathrm{9}=\mathrm{0} \\ $$$$\mathrm{are}\:\mathrm{in}\:\mathrm{AP} \\ $$ Commented by Her_Majesty last updated on…

Question Number 41305 by sameer12 last updated on 05/Aug/18 $$\begin{bmatrix}{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}\\{\mathrm{3}}&{\mathrm{4}}&{\mathrm{5}}\\{\mathrm{5}}&{\mathrm{6}}&{\mathrm{7}}\end{bmatrix} \\ $$$${find}\:{determinant}\:{of}\:{given}\:{matrix}? \\ $$ Commented by MrW3 last updated on 05/Aug/18 $${row}\:\mathrm{3}\:−{row}\:\mathrm{2}: \\ $$$$\begin{bmatrix}{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}\\{\mathrm{3}}&{\mathrm{4}}&{\mathrm{5}}\\{\mathrm{2}}&{\mathrm{2}}&{\mathrm{2}}\end{bmatrix} \\…

Question Number 106695 by bobhans last updated on 06/Aug/20 $$\:\:\:\:#\mathrm{bobhans}# \\ $$$$\mathrm{3}^{\mathrm{x}} −\mathrm{2}^{\mathrm{x}+\mathrm{1}} \:\leqslant\:\sqrt{\mathrm{2}.\mathrm{9}^{\mathrm{x}} −\mathrm{10}.\mathrm{6}^{\mathrm{x}} +\mathrm{2}^{\mathrm{2x}+\mathrm{3}} } \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{set} \\ $$ Answered by bemath last…