Category: Arithmetic

Question Number 17767 by Joel577 last updated on 10/Jul/17 $$\underset{n=1}{\sum ^{30}}(n^2+1)=$$$$\left(\mathrm{A}\right)\underset{n=1}{\sum ^{15}}(2n^2+30n+224)$$$$\left(\mathrm{B}\right)\underset{n=1}{\sum ^{15}}(2n^2+30n+225)$$$$\left(\mathrm{C}\right)\:\underset{{n}\:=\:\mathrm{1}}…

Question Number 148780 by Jonathanwaweh last updated on 31/Jul/21 Answered by Kamel last updated on 31/Jul/21 $$$$$$\Omega=\underset{{n}=\mathrm{2}} {\overset{+\infty} {\prod}}{e}\left(\mathrm{1}−\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)^{{n}^{\mathrm{2}} } ={e}^{\underset{{n}=\mathrm{2}} {\overset{+\infty}…

Question Number 83242 by peter frank last updated on 29/Feb/20 Commented by john santu last updated on 29/Feb/20 $$\left(\mathrm{4b}\right)\:\underset{\mathrm{r}\:=\:\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{r}\left(\mathrm{r}+\mathrm{1}\right)\:=\:\underset{\mathrm{r}\:=\:\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{r}^{\mathrm{2}} \:+\:\underset{\mathrm{r}\:=\:\mathrm{1}} {\overset{\mathrm{n}}…

Question Number 148753 by Jonathanwaweh last updated on 30/Jul/21 Answered by mathmax by abdo last updated on 31/Jul/21 $$\mathrm{A}_{\mathrm{n}} =\prod_{\mathrm{k}=\mathrm{2}} ^{\mathrm{n}} \:\mathrm{e}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{k}^{\mathrm{2}} }\right)^{\mathrm{k}^{\mathrm{2}} } \:\Rightarrow\mathrm{A}_{\mathrm{n}}…

Question Number 83188 by john santu last updated on 28/Feb/20 $$\mathrm{If}\underset{\mathrm{a}=0}{\sum ^{\mathrm{n}-1}}(2\mathrm{a}+1){\mathrm{x}}^2+({\mathrm{n}}^2+4\mathrm{n}-5)\mathrm{x}+16$$$$=0\mathrm{is}\mathrm{a}\mathrm{perfect}\mathrm{square}\mathrm{such}\mathrm{that}$$$$\mathrm{n}\in {\mathbb{Z}}^{+}.\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{value}\mathrm{of}$$$$\mathrm{x}+\mathrm{n}?$$ Answered…