Category: Arithmetic

Question Number 15671 by tawa tawa last updated on 12/Jun/17 $$\mathrm{Prove}\mathrm{by}\mathrm{mathematcal}\mathrm{induction}\mathrm{that}$$$$1+\frac{1}{1+2}+\frac{1}{1+2+3}+\dots +\frac{1}{1+2+3+\dots \mathrm{n}}=\frac{2\mathrm{n}}{\mathrm{n}+1}$$ Answered by icyfalcon999 last updated on 12/Jun/17 $$1)\mathrm{proving}\mathrm{that}\mathrm{the}\mathrm{statement}\mathrm{true}\mathrm{when}\mathrm{n}=1$$$$\mathrm{R}.\mathrm{H}.\mathrm{S}.=\frac{\mathrm{2}\left(\mathrm{1}\right)}{\mathrm{1}+\mathrm{1}}=\frac{\mathrm{2}}{\mathrm{2}}=\mathrm{1}=\mathrm{L}.\mathrm{H}.\mathrm{S}.…

Question Number 80786 by M±th+et£s last updated on 06/Feb/20 Commented by mind is power last updated on 06/Feb/20 $$iwilltrynoteasy!$$ Commented by mr W…

Question Number 146174 by ArielVyny last updated on 11/Jul/21 $$calculer{lim}_{x\to 1}(x-1)\sum _{n⩾0}\frac{1}{n^x}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 146130 by Huy last updated on 11/Jul/21 $$(2^{\mathrm{k}}+1)(3^{\mathrm{k}}+2)\equiv 0(\mathrm{mod}\mathrm{k}+5)$$$$\min \mathrm{k}=?(\mathrm{k}\in \mathbb{N})$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 145982 by ArielVyny last updated on 10/Jul/21 $$\sum _{n⩾0}{(-\frac{1}{81})}^n\mathrm{\Gamma }(3n+3)=??$$ Answered by Olaf_Thorendsen last updated on 10/Jul/21 $$\mathrm{diverges}$$ Terms…