Question Number 24540 by Tinkutara last updated on 20/Nov/17 $${Prove}\:{that} \\ $$$$\left({i}\right)\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{n}^{\mathrm{2}} }{{n}!}=\mathrm{2}{e}. \\ $$$$\left({ii}\right)\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{n}^{\mathrm{3}} }{{n}!}=\mathrm{5}{e}. \\ $$$$\left({iii}\right)\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{n}^{\mathrm{4}} }{{n}!}=\mathrm{15}{e}.…
Question Number 155594 by mathdanisur last updated on 02/Oct/21 Answered by ghimisi last updated on 02/Oct/21 $$\Leftrightarrow\Sigma\left(\sqrt{{x}^{\mathrm{4}} +{y}^{\mathrm{4}} }−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} +\left(\mathrm{2}−\sqrt{\mathrm{2}}\right){xy}\right)\geqslant\mathrm{0} \\ $$$$\sqrt{{x}^{\mathrm{4}} +{y}^{\mathrm{4}} }−{x}^{\mathrm{2}}…
Question Number 90048 by jagoll last updated on 21/Apr/20 $$\mathrm{5}^{\sqrt{\mathrm{x}}} \:−\mathrm{5}^{\mathrm{x}−\mathrm{7}} \:=\:\mathrm{100} \\ $$ Answered by jagoll last updated on 21/Apr/20 Terms of Service Privacy…
Question Number 155585 by mathdanisur last updated on 02/Oct/21 $$\mathrm{Evaluate}\:\mathrm{the}\:\mathrm{limit}\:\mathrm{and}\:\mathrm{prove}\:\mathrm{by}\:\mathrm{the} \\ $$$$\varepsilon−\delta\:\mathrm{definition}\:\mathrm{that}\:\mathrm{as}\:\mathrm{n}\rightarrow\infty\:\mathrm{for}\:\mathrm{z}\geqslant\mathrm{1} \\ $$$$\left(\mathrm{2}\sqrt[{\boldsymbol{\mathrm{n}}}]{\mathrm{z}}\:−\:\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}} \:\rightarrow\:\mathrm{z}^{\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 155572 by peter frank last updated on 02/Oct/21 $$\mathrm{Find}\:\mathrm{Z}^{\mathrm{4}} =\mathrm{1}. \\ $$$$\mathrm{Hence}\:\mathrm{show}\:\mathrm{that}\:\mathrm{1}+\mathrm{w}+\mathrm{w}^{\mathrm{2}} +\mathrm{w}^{\mathrm{3}} =\mathrm{0} \\ $$ Answered by puissant last updated on 02/Oct/21…
Question Number 90038 by frc2crc last updated on 21/Apr/20 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{H}_{{n}} }{{n}^{{k}} }={S}_{{k}} \:\:\:\:\:\:\:{H}_{{q}} =\underset{{p}=\mathrm{1}} {\overset{{q}} {\sum}}\frac{\mathrm{1}}{{p}} \\ $$$${Is}\:{there}\:{a}\:{simple}\:{from}\:{for}\:{S}_{{k}} \\ $$ Terms of Service…
Question Number 155568 by mr W last updated on 02/Oct/21 $${for}\:{a},{b},{c},{d},{e}\:\in{R}\:{and}\:{a}+{b}+{c}+{d}+{e}=\mathrm{5} \\ $$$${find}\:{the}\:{minimum}\:{value}\:{of}\: \\ $$$${a}^{\mathrm{2}} +\mathrm{2}{b}^{\mathrm{2}} +\mathrm{3}{c}^{\mathrm{2}} +\mathrm{4}{d}^{\mathrm{2}} +\mathrm{5}{e}^{\mathrm{2}} =? \\ $$ Answered by qaz…
Question Number 90030 by peter frank last updated on 21/Apr/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 155545 by mathdanisur last updated on 02/Oct/21 $$\mathrm{Solve}\:\mathrm{in}\:\mathbb{R} \\ $$$$\frac{\mathrm{5x}}{\:\sqrt{\mathrm{5x}^{\mathrm{2}} \:+\:\mathrm{4}}\:+\:\mathrm{7}\sqrt{\mathrm{x}}}\:+\:\frac{\mathrm{x}\:+\:\mathrm{2}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{3x}\:-\:\mathrm{18}}\:+\:\mathrm{2}\sqrt{\mathrm{x}}} \\ $$ Commented by Rasheed.Sindhi last updated on 02/Oct/21 $$=\mathrm{0}? \\…
Question Number 155547 by mathdanisur last updated on 02/Oct/21 $$\mathrm{let}\:\:\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0}\:\:\mathrm{and}\:\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{3} \\ $$$$\mathrm{find}\:\mathrm{min}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{expression}: \\ $$$$\mathrm{S}\:=\:\mathrm{abc}\:+\:\left(\mathrm{a}-\mathrm{1}\right)^{\mathrm{2}} \:+\:\left(\mathrm{b}-\mathrm{1}\right)^{\mathrm{2}} \:+\:\left(\mathrm{c}-\mathrm{1}\right)^{\mathrm{2}} \\ $$ Answered by ghimisi last updated on 02/Oct/21…