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n-0-1-n-1-n-n-

Question Number 205774 by mnjuly1970 last updated on 30/Mar/24 $$ \\ $$$$\:\:\:\:\:\:−−−−−−− \\ $$$$\:\:\:\:\:\Omega\:=\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\:\left(−\mathrm{1}\right)^{\:{n}} }{\left(−\mathrm{1}\right)^{\:{n}} \:−{n}}\:=\:?\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:−−−−−−− \\ $$ Answered by MathedUp…

If-x-y-z-gt-0-and-xyz-1-Prove-that-2-x-2-1-xz-1-xy-2-y-2-1-yz-1-xy-2-z-2-1-xz-1-yz-3-2-

Question Number 205770 by hardmath last updated on 30/Mar/24 $$\mathrm{If}\:\:\mathrm{x},\mathrm{y},\mathrm{z}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{xyz}\:=\:\mathrm{1} \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\frac{\left(\sqrt{\mathrm{2}}\mathrm{x}\right)^{\mathrm{2}} }{\left(\mathrm{1}+\mathrm{xz}\right)\left(\mathrm{1}+\mathrm{xy}\right)}\:+\:\frac{\left(\sqrt{\mathrm{2}}\mathrm{y}\right)^{\mathrm{2}} }{\left(\mathrm{1}+\mathrm{yz}\right)\left(\mathrm{1}+\mathrm{xy}\right)}\:+\:\frac{\left(\sqrt{\mathrm{2}}\mathrm{z}\right)^{\mathrm{2}} }{\left(\mathrm{1}+\mathrm{xz}\right)\left(\mathrm{1}+\mathrm{yz}\right)}\:\geqslant\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact:…

a-b-c-a-b-c-1-a-2-1-b-c-b-2-1-a-c-c-2-1-a-b-k-find-k-max-hint-inequality-cauchy-schwarz-

Question Number 205767 by lmcp1203 last updated on 30/Mar/24 $$ \\ $$$${a},{b},{c}\:\in\Re^{+} \:\: \\ $$$${a}+{b}+{c}=\mathrm{1} \\ $$$$\:\:\:{a}^{\mathrm{2}} /\left(\mathrm{1}+{b}+{c}\right)\:+\:{b}^{\mathrm{2}} /\left(\mathrm{1}+{a}+{c}\right)\:\:+\:{c}^{\mathrm{2}} /\left(\mathrm{1}+{a}+{b}\right)\geqslant{k} \\ $$$${find}\:\:\:{k}\:{max}. \\ $$$${hint}\::\:{inequality}\:{cauchy}\:{schwarz} \\…

whats-the-suficient-condition-to-became-the-question-2-1-a-i-i-1-a-i-1-a-i-1-d-i-i-k-lt-0-

Question Number 205749 by mokys last updated on 29/Mar/24 $${whats}\:{the}\:{suficient}\:{condition}\:{to}\:{became}\:{the}\:{question}\: \\ $$$$ \\ $$$$\sigma^{\mathrm{2}} \left(\mathrm{1}−{a}_{{i}} \right)\left[\lambda_{{i}} \left(\mathrm{1}+{a}_{{i}} \right)−\left(\mathrm{1}−{a}_{{i}} \right)\left(\mathrm{1}−{d}_{{i}} \right)+\left(\lambda_{{i}} +{k}\right)\right]\:<\:\mathrm{0}\: \\ $$ Terms of…

0-1-1-e-2x-dx-

Question Number 205750 by MetaLahor1999 last updated on 29/Mar/24 $$\int_{\mathrm{0}} ^{+\infty} \frac{\mathrm{1}}{\mathrm{1}+{e}^{\mathrm{2}{x}} }{dx}=? \\ $$ Commented by mokys last updated on 29/Mar/24 $$=\:−\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\:\infty} \:\frac{−\mathrm{2}{e}^{−\mathrm{2}{x}}…