Category: Arithmetic

Question Number 215845 by Tawa11 last updated on 19/Jan/25 $$1,3,-1,-3,-7,-21,-25,\mathrm{\_}\mathrm{\_}\mathrm{\_},\mathrm{\_}\mathrm{\_}\mathrm{\_},\mathrm{\_}\mathrm{\_}\mathrm{\_}$$$$$$$$\mathrm{Next}\mathrm{three}\mathrm{terms}??$$ Commented by mr W last updated on 20/Jan/25 $${this}\:{is}\:{a}\:{game},\:{not}\:{mathematics}!!!…

Question Number 215229 by Mingma last updated on 01/Jan/25 Answered by devdutt last updated on 01/Jan/25 $$1.f\left(\frac{k}{n}\right)=\frac{n^{2025}}{n^{2025}+k^{2025}}$$$$$$$$\mathrm{2}.\:{f}\left(\frac{{k}}{{n}}\right)+{f}\left(\frac{{n}}{{k}}\right)\:=\:\mathrm{1},\: \…

Question Number 215232 by Mingma last updated on 01/Jan/25 Answered by devdutt last updated on 01/Jan/25 $$\ln 3\sqrt{5}+\ln x\log {}_{45}x=2\ln x$$$$\Rightarrow \ln 3\sqrt{5}+\frac{\ln {}^{2}x}{\ln 45}=2\ln x$$$$\Rightarrow\:\mathrm{ln}\:^{\mathrm{2}} {x}\:−\:\mathrm{2ln}\:\mathrm{45}\:\mathrm{ln}\:{x}\:+\:\mathrm{ln}\:\mathrm{3}\sqrt{\mathrm{5}}\:\mathrm{ln}\:\mathrm{45}\:=\:\mathrm{0} \…

Question Number 214622 by Frangg last updated on 13/Dec/24 Answered by Rasheed.Sindhi last updated on 14/Dec/24 $$\underset{―}{Iftodeterminex:}$$$$△\mathrm{ABE}\sim △\mathrm{DCE}$$$$\frac{\mathrm{AB}}{\mathrm{DC}}=\frac{\mathrm{AE}}{\mathrm{DE}}$$$$\frac{19}{6}=\frac{2\mathrm{x}+8}{\mathrm{x}-2}$$$$\mathrm{19x}−\mathrm{38}=\mathrm{12x}+\mathrm{48}…

Question Number 213802 by efronzo1 last updated on 17/Nov/24 Answered by A5T last updated on 17/Nov/24 $$t_1=k-1;t_2=k$$$$t_3=\frac{5k+1}{25k-25};t_4=\frac{\frac{10k-4}{5k-5}}{25k}=\frac{10k-4}{125k(k-1)}$$$${t}_{\mathrm{5}}…