Category: Arithmetic

Question Number 153070 by bobhans last updated on 04/Sep/21 $$Findthesolutionsetofinequality$$$$\sqrt{3x+4}⩾x-2$$ Answered by Rasheed.Sindhi last updated on 04/Sep/21 $$\sqrt{3x+4}⩾x-2$$$$\:\:\:\:\:\:\:\left(\:\sqrt{\mathrm{3}{x}+\mathrm{4}}\:\geqslant\:{x}−\mathrm{2}\:\right)^{\mathrm{2}} \…

Question Number 21738 by Joel577 last updated on 02/Oct/17 $$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{last}\mathrm{digit}\mathrm{from}\mathrm{the}\mathrm{sum}\mathrm{of}$$$$1.2^1+2.2^2+3.2^3+\dots +50.2^{50}?$$ Answered by $@ty@m last updated on 02/Oct/17…

Question Number 87179 by peter frank last updated on 03/Apr/20 Commented by peter frank last updated on 03/Apr/20 $$qn2$$ Commented by Rio Michael…

Question Number 21502 by 786786AM last updated on 25/Sep/17 $$\mathrm{In}\mathrm{an}\mathrm{A}.\mathrm{P},\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{p}\mathrm{terms}\mathrm{is}\mathrm{q}\mathrm{and}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{q}\mathrm{terms}\mathrm{is}\mathrm{p}.$$$$\mathrm{Prove}\mathrm{that}\mathrm{the}\mathrm{sum}\mathrm{of}(\mathrm{p}+\mathrm{q})\mathrm{terms}\mathrm{is}-(\mathrm{p}+\mathrm{q}).$$ Answered by $@ty@mlastupdatedon25/Sep/17$$ATQ$$$$\boldsymbol{\mathrm{S}}_{{p}} ={q}…

Question Number 152496 by mathdanisur last updated on 28/Aug/21 Answered by qaz last updated on 29/Aug/21 $$\underset{\mathrm{n}=1}{\sum ^{\mathrm{\infty }}}\frac{{\mathrm{x}}^{4\mathrm{n}}}{\left(4\mathrm{n}\right)!}=\frac{{\mathrm{x}}^4}{4!}+\frac{{\mathrm{x}}^8}{8!}+\frac{{\mathrm{x}}^{12}}{12!}+\dots$$$$=\frac{\mathrm{1}}{\mathrm{2}}\left[\left(\mathrm{1}−\frac{\mathrm{x}^{\mathrm{2}}…