Category: Algebra

Question Number 121246 by benjo_mathlover last updated on 06/Nov/20 $$\underset{\mathrm{k}=1}{\sum ^{49}}\frac{1}{\sqrt{\mathrm{k}+\sqrt{{\mathrm{k}}^2-1}}}?$$ Answered by liberty last updated on 06/Nov/20 $$\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{k}+\sqrt{\mathrm{k}^{\mathrm{2}} −\mathrm{1}}}}\:=\:\frac{\mathrm{1}}{\:\sqrt{\left(\sqrt{\frac{\mathrm{k}+\mathrm{1}}{\mathrm{2}}}+\sqrt{\frac{\mathrm{k}−\mathrm{1}}{\mathrm{2}}}\right)^{\mathrm{2}} }}…

Question Number 55685 by tm888 last updated on 02/Mar/19 $$proofthat$$$$\underset{i=1}{\sum ^n}\frac{a_i}{a_i-x}=2015hasexactlynreal$$$$roots.o<a_1\dots .<a_n$$ Answered by mr W…

Question Number 55671 by gunawan last updated on 01/Mar/19 $$\mathrm{Let}\mathrm{z}\in \mathbb{C},\mathrm{so}\mid 1+z^2\mid <1.$$$$\mathrm{Prove}\mathrm{that}2\mid 1+z^2\mid ⩾1$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 186732 by mr W last updated on 09/Feb/23 Answered by mr W last updated on 09/Feb/23 $${let}^{\prime }sgenerallyfindthemaximumof$$$${S}={a}_{\mathrm{1}} +{a}_{\mathrm{2}} +…+{a}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}}…

Question Number 186701 by Mingma last updated on 08/Feb/23 Commented by aba last updated on 08/Feb/23 $$\frac{4}{5}$$ Commented by Mingma last updated on…