Category: Arithmetic

Question Number 68773 by rajesh4661kumar@gmail.com last updated on 15/Sep/19 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 3204 by Filup last updated on 07/Dec/15 $$\underset{i=1}{\prod ^n}i!=1\times \left(1\times 2\right)\times \dots \times (1\times 2\times \dots \times n)$$$$=1^n{2}^{n-1}{3}^{n-2}\dots {(n-1)}^{2}n$$$$\therefore\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\prod}}{i}!=\underset{{i}=\mathrm{1}} {\overset{{n}} {\prod}}\left({n}−{i}+\mathrm{1}\right)^{{i}} \…

Question Number 3198 by Filup last updated on 07/Dec/15 $$\underset{i=a}{\prod ^n}i=?\mathrm{for}\mid i\mid <1,a\in \mathbb{R}$$ Commented by Filup last updated on 07/Dec/15 $$=\frac{1}{a}\times \frac{1}{a+1}\times \dots \times \frac{1}{n}$$$$=\frac{\mathrm{1}}{\left(\frac{{n}!}{\left({a}−\mathrm{1}\right)!}\right)} \…

Question Number 68710 by peter frank last updated on 15/Sep/19 Commented by Prithwish sen last updated on 15/Sep/19 $$\mathrm{x}+\mathrm{y}=0\dots \dots .\left(\mathrm{i}\right)$$$$\mathrm{x}-\mathrm{y}=-4\dots \dots \left(\mathrm{ii}\right)$$$$\mathrm{solving}\mathrm{x}=-2,\mathrm{y}=2$$$$\therefore\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{center}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{circle}}\:\boldsymbol{\mathrm{is}}\:\left(−\mathrm{2},\mathrm{2}\right)…

Question Number 3105 by prakash jain last updated on 04/Dec/15 $$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{next}\mathrm{term}\mathrm{in}\mathrm{the}\mathrm{below}\mathrm{sequence}$$$$1,3,9,27,81,243,729,2123,5857,?$$ Commented by Filup last updated on 04/Dec/15 $$\mathrm{3}^{\mathrm{10}} ? \…