Question Number 144196 by qaz last updated on 23/Jun/21 $$\mathrm{Let}\:\mathrm{a},\mathrm{b},\mathrm{c}>\mathrm{0}\:\mathrm{and}\:\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{3}.\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{1}+\mathrm{a}^{\mathrm{2}} \right)\left(\mathrm{1}+\mathrm{b}^{\mathrm{2}} \right)\left(\mathrm{1}+\mathrm{c}^{\mathrm{2}} \right)\leqslant\left(\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\mathrm{abc}}}\right)^{\mathrm{3}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 144199 by qaz last updated on 23/Jun/21 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}+\frac{\mathrm{1}^{\mathrm{2}} }{\mathrm{6}+\frac{\mathrm{3}^{\mathrm{2}} }{\mathrm{6}+\frac{\mathrm{5}^{\mathrm{2}} }{\mathrm{6}+\frac{\mathrm{7}^{\mathrm{2}} }{\mathrm{6}+\frac{\mathrm{9}^{\mathrm{2}} }{\mathrm{6}+…}}}}}=\frac{\mathrm{2}}{\mathrm{1}+\frac{\mathrm{1}×\mathrm{2}}{\mathrm{1}+\frac{\mathrm{2}×\mathrm{3}}{\mathrm{1}+\frac{\mathrm{3}×\mathrm{4}}{\mathrm{1}+\frac{\mathrm{4}×\mathrm{5}}{\mathrm{1}+\frac{\mathrm{5}×\mathrm{6}}{\mathrm{1}+…}}}}}} \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 78650 by Pratah last updated on 19/Jan/20 Commented by mr W last updated on 19/Jan/20 $$={x}^{\mathrm{2}} +\mathrm{1} \\ $$ Commented by john santu…
Question Number 144190 by mathdanisur last updated on 22/Jun/21 $$\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{5}{n}}{{n}^{\mathrm{2}} \:+\:\mathrm{3}}\:=\:? \\ $$ Answered by mathmax by abdo last updated on 23/Jun/21 $$\mathrm{this}\:\mathrm{serie}\:\mathrm{is}\:\mathrm{divergent}\:\mathrm{due}\:\mathrm{to}\:\frac{\mathrm{5n}}{\mathrm{n}^{\mathrm{2}}…
Question Number 144177 by mathdanisur last updated on 22/Jun/21 Answered by mindispower last updated on 22/Jun/21 $${diverge}\: \\ $$$${x}\rightarrow\mathrm{0} \\ $$$$\mathrm{1}−{cos}\left({x}\right)+{x}^{\mathrm{2}} \sim\frac{\mathrm{3}{x}^{\mathrm{2}} }{\mathrm{2}} \\ $$$${x}\rightarrow\frac{\mathrm{2}}{\mathrm{3}{x}^{\mathrm{2}}…
Question Number 144170 by mathdanisur last updated on 22/Jun/21 Answered by Olaf_Thorendsen last updated on 22/Jun/21 $$\mathrm{P}\left({x}\right)\:=\:\underset{{k}=\mathrm{0}} {\overset{\mathrm{4}} {\sum}}{a}_{{k}} {x}^{{k}} \\ $$$$\mathrm{P}\left({m}\right)\:=\:\underset{{k}=\mathrm{0}} {\overset{\mathrm{4}} {\sum}}{a}_{{k}} {m}^{{k}}…
Question Number 144156 by mathdanisur last updated on 22/Jun/21 Commented by mitica last updated on 22/Jun/21 $${x}=\mathrm{2},{y}=\mathrm{8}\:{false} \\ $$$$,,\leqslant,,\:{or},,\geqslant,, \\ $$ Commented by mathdanisur last…
Question Number 13081 by 433 last updated on 13/May/17 $$\begin{cases}{{x}+{y}+{z}=\left[\mathrm{1}\right]_{\mathrm{5}} }\\{{xy}=\left[\mathrm{2}\right]_{\mathrm{5}} }\\{{yz}=\left[\mathrm{1}\right]_{\mathrm{5}} }\end{cases} \\ $$$${Solve}\:{system}\:{on}\:\mathbb{Z}_{\mathrm{5}} \\ $$ Answered by RasheedSindhi last updated on 14/May/17 $$\:^{{Rasheed}\:{Soomro}}…
Question Number 144148 by bobhans last updated on 22/Jun/21 $$\begin{cases}{\mathrm{2ln}\:\mathrm{x}+\mathrm{ln}\:\mathrm{y}\:=\:\mathrm{2}}\\{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}\:=\:\mathrm{e}^{\mathrm{2}} +\mathrm{1}}\end{cases} \\ $$ Answered by EDWIN88 last updated on 22/Jun/21 $$\:\begin{cases}{\mathrm{x}^{\mathrm{2}} \mathrm{y}\:=\:\mathrm{e}^{\mathrm{2}} }\\{\mathrm{x}^{\mathrm{2}} +\mathrm{y}\:=\:\mathrm{e}^{\mathrm{2}}…
Question Number 144132 by islamo last updated on 21/Jun/21 Answered by ArielVyny last updated on 22/Jun/21 $$\underset{{n}\geqslant\mathrm{0}} {\sum}\frac{\mathrm{1}}{{ln}\left({n}\right)^{{ln}\left({n}\right)} }\backsim\underset{{n}\geqslant\mathrm{0}} {\sum}\frac{\mathrm{1}}{{n}^{{n}} }\:\left({CV}\right) \\ $$ Answered by…