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Category: Arithmetic

show-that-U-n-1-nx-n-n-1-2-x-2-n-n-1-n-2-3-x-3-for-which-U-n-1-x-n-

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…

bemath-What-is-m-so-the-roots-of-x-4-m-2-x-2-9-0-are-in-AP-

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…

Please-any-geometry-proof-on-shortest-distance-between-two-places-Topic-longitude-and-latitude-

Question Number 106844 by I want to learn more last updated on 07/Aug/20 $$\mathrm{Please}\:\mathrm{any}\:\mathrm{geometry}\:\mathrm{proof}\:\mathrm{on}\:\mathrm{shortest}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{two} \\ $$$$\mathrm{places}\:\:\:\left(\mathrm{Topic}\:\mathrm{longitude}\:\mathrm{and}\:\mathrm{latitude}\right). \\ $$ Commented by mathdave last updated on 07/Aug/20…

1-2-3-3-4-5-5-6-7-find-determinant-of-given-matrix-

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} \\…