Category: Arithmetic

Question Number 70417 by aliesam last updated on 04/Oct/19 Answered by MJS last updated on 04/Oct/19 $$\mathrm{just}\mathrm{use}\mathrm{formulas}$$$$\mathrm{sphere}:V=\frac{4\pi }{3}{r}^3;S=4\pi r^2$$$$\mathrm{cylinder}:V=\pi r^{2}h$$$$\:\:\:\:\:{S}=\mathrm{2}×\mathrm{circle}+\mathrm{lateral}=\mathrm{2}\pi{r}^{\mathrm{2}}…

Question Number 135889 by Ar Brandon last updated on 16/Mar/21 $$1\mathrm{\setminus }\mathrm{If}\mathrm{A}\mathrm{and}\mathrm{B}\mathrm{are}\mathrm{sets}\mathrm{define}\mathrm{their}\mathrm{scheffer}\mathrm{product}\mathrm{A}\ast \mathrm{B}\mathrm{by}\mathrm{A}\ast \mathrm{B}=\mathrm{A}\ast \cap \mathrm{B}\ast$$$$\mathrm{Prove}\mathrm{by}\mathrm{definitions}\mathrm{that}(\mathrm{A}\ast \mathrm{B})\ast (\mathrm{A}\ast \mathrm{B})=\mathrm{A}\cup \mathrm{B}$$$$$$$$2\mathrm{\setminus }\mathrm{State}\mathrm{the}\mathrm{strong}\mathrm{principle}\mathrm{of}\mathrm{mathematical}\mathrm{induction}.$$$$\mathrm{Suppose}\mathrm{that}{\mathrm{a}}_1=1,{\mathrm{a}}_2=3$$$$\mathrm{a}_{\mathrm{k}} =\mathrm{a}_{\mathrm{k}−\mathrm{2}} +\mathrm{2a}_{\mathrm{k}−\mathrm{1}}…

Question Number 4704 by lakshaysethi039 last updated on 25/Feb/16 $$If{a}_1,a_2,\dots \dots \dots a_{n}beanarithmeticprogression,$$$$thenshowthat$$$$\frac{\mathrm{1}}{{a}_{\mathrm{1}} {a}_{{n}} }\:+\:\frac{\mathrm{1}}{{a}_{\mathrm{2}} {a}_{{n}−\mathrm{1}} }\:+\:\frac{\mathrm{1}}{{a}_{\mathrm{3}} {a}_{{n}−\mathrm{2}} }\:+………….+\frac{\mathrm{1}}{{a}_{{n}} {a}_{\mathrm{1}} }\:…

Question Number 4645 by FilupSmith last updated on 18/Feb/16 $$S=\underset{i=1}{\prod ^x}\left(i^{\frac{1}{2}(x-i+1)(x-i+2)}\right),(x,i)\in \mathbb{Z}$$$$$$$$\mathrm{Prove}\mathrm{that}S\in \mathbb{Z}$$ Answered by Yozzii last updated on…

Question Number 135672 by Raxreedoroid last updated on 14/Mar/21 $$\mathrm{Write}\underset{k=1}{\sum ^{n-2}}{kx}^{k-1}\mathrm{in}\mathrm{terms}n$$ Answered by Olaf last updated on 15/Mar/21 $${a}^{{n}} −{b}^{{n}} \:=\:\left({a}−{b}\right)\left({a}^{{n}−\mathrm{1}}…