Category: Arithmetic

Question Number 148677 by nadovic last updated on 30/Jul/21 $$\mathrm{A}\mathrm{series}\mathrm{of}\mathrm{natural}\mathrm{numbers}\mathrm{are}$$$$\mathrm{grouped}\mathrm{as}1+(2+3)+(4+5+6)+\dots$$$$\mathrm{such}\mathrm{that}\mathrm{the}rth\mathrm{group}\mathrm{contains}r$$$$\mathrm{terms}.\mathrm{Show}\mathrm{that}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{the}$$$$\mathrm{numbers}\mathrm{in}\mathrm{the}(2r-1)th\mathrm{group}\mathrm{is}$$$${\mathit{r}}^4-{(\mathit{r}-1)}^4.$$ Answered…

Question Number 148559 by Jonathanwaweh last updated on 29/Jul/21 Answered by Kamel last updated on 29/Jul/21 $$a=3k+r,b=3k^{\prime }+r^{\prime }0⩽r<3,0⩽r^{\prime }<3.$$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} =\mathrm{3}{c}=\mathrm{9}\left({k}^{\mathrm{2}} +{k}'^{\mathrm{2}} \right)+\mathrm{6}\left({kr}+{k}'{r}'\right)+{r}^{\mathrm{2}} +{r}'^{\mathrm{2}} \…

Question Number 148483 by puissant last updated on 28/Jul/21 $$\mathrm{Soit}\mathrm{f}\mathrm{une}\mathrm{fonction}\mathrm{continu}\mathrm{sur}\mathbb{R}$$$$\mathrm{et}\mathrm{non}\mathrm{identiquement}\mathrm{nulle},$$$$\mathrm{\forall }\mathrm{x},{\mathrm{x}}^{\prime }\in \mathbb{R},\mathrm{f}(\mathrm{x}-{\mathrm{x}}^{\prime })+\mathrm{f}(\mathrm{x}+{\mathrm{x}}^{\prime })=2\mathrm{f}\left(\mathrm{x}\right)\mathrm{f}\left({\mathrm{x}}^{\prime }\right)$$$$\mathrm{montrer}\mathrm{que}:$$$$\mathrm{f}\left(0\right)=1\mathrm{et}\mathrm{f}\left(\mathrm{x}\right)=\mathrm{f}(-\mathrm{x})..$$ Answered by Olaf_Thorendsen last updated…

Question Number 148398 by puissant last updated on 27/Jul/21 Answered by Olaf_Thorendsen last updated on 27/Jul/21 $$1.{\mathrm{C}}_1=7l\mathrm{et}{\mathrm{C}}_2=4l$$$$$$$$\bullet \mathrm{Etape}1.$$$$\mathrm{Je}\:\mathrm{remplis}\:\mathrm{C}_{\mathrm{1}}…

Question Number 148368 by bouchrag last updated on 27/Jul/21 Terms of Service Privacy Policy Contact: info@tinkutara.com