Category: Algebra

Question Number 24010 by Tinkutara last updated on 11/Nov/17 $$\mathrm{Prove}\:\mathrm{that}\:\underset{{r}=\mathrm{1}} {\overset{\mathrm{2}{n}−\mathrm{1}} {\sum}}\left(−\mathrm{1}\right)^{{r}−\mathrm{1}} \centerdot\frac{{r}}{\:^{\mathrm{2}{n}} {C}_{{r}} }\:=\:\frac{{n}}{{n}\:+\:\mathrm{1}}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 155069 by mathdanisur last updated on 24/Sep/21 $$\mathrm{if}\:\:\mathrm{x};\mathrm{y};\mathrm{z}>\mathrm{0}\:\:\mathrm{such}\:\mathrm{that}\:\:\mathrm{x}+\mathrm{y}+\mathrm{z}=\mathrm{3} \\ $$$$\mathrm{and}\:\:\mathrm{0}\leqslant\boldsymbol{\lambda}\leqslant\mathrm{1}\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{x}}{\mathrm{y}^{\mathrm{2}} +\lambda}\:+\:\frac{\mathrm{y}}{\mathrm{z}^{\mathrm{2}} +\lambda}\:+\:\frac{\mathrm{z}}{\mathrm{x}^{\mathrm{2}} +\lambda}\:\geqslant\:\frac{\mathrm{3}}{\lambda+\mathrm{1}} \\ $$ Terms of Service Privacy Policy Contact:…

Question Number 155056 by mathdanisur last updated on 24/Sep/21 Answered by mr W last updated on 24/Sep/21 $${BF}^{\mathrm{2}} ={AB}^{\mathrm{2}} +\left(\sqrt{\mathrm{2}}{AC}\right)^{\mathrm{2}} +\mathrm{2}×{AB}×\sqrt{\mathrm{2}}{AC}×\mathrm{cos}\:\left({A}+\frac{\pi}{\mathrm{4}}\right)\:\:\:..\left({i}\right) \\ $$$${CD}^{\mathrm{2}} ={AC}^{\mathrm{2}} +\left(\sqrt{\mathrm{2}}{AB}\right)^{\mathrm{2}}…

Question Number 89505 by AnsarFawaz last updated on 17/Apr/20 Answered by TANMAY PANACEA. last updated on 17/Apr/20 $$\left.{i}\right){two}\:\:{at}\:+\infty\:\:{and}\:−\infty \\ $$$$\left.{ii}\right){one}\: \\ $$$$\left.{iii}\right){three} \\ $$ Terms…

Question Number 23953 by NECx last updated on 10/Nov/17 $${find}\:{the}\:{nth}\:{term}\:{of}\:{the}\:{sequence} \\ $$$$\mathrm{4},\:\mathrm{9},\:\mathrm{16},\:\mathrm{45},\:\mathrm{76} \\ $$$$ \\ $$$${please}\:{help} \\ $$ Commented by prakash jain last updated on…