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Category: Arithmetic

lim-x-n-ln-1-n-find-the-limit-

Question Number 41855 by 123456780 last updated on 14/Aug/18 $$\underset{{x}\rightarrow+\infty\:\:} {\mathrm{lim}}\frac{\mathrm{n}!}{\mathrm{ln}\:\left(\mathrm{1}+\mathrm{n}!\right)} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{limit} \\ $$ Commented by prof Abdo imad last updated on 14/Aug/18 $${let}\:{put}\:{p}={n}!\:\Rightarrow\:\:\frac{{n}!}{{ln}\left(\mathrm{1}+{n}!\right)}\:=\frac{{p}}{{ln}\left(\mathrm{1}+{p}\right)}…

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…