Question Number 62003 by maxmathsup by imad last updated on 13/Jun/19 $${let}\:\xi\left({x}\right)\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{{x}} }\:\:\:{with}\:{x}>\mathrm{1}\:\:{prove}\:{that}\:\:\xi\left({x}\right)\:=\prod_{{p}\:{prime}} \:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}−{p}^{−{x}} } \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 192979 by Red1ight last updated on 01/Jun/23 $$\mathrm{Can}\:\mathrm{this}\:\mathrm{be}\:\mathrm{optimized}\:\left(\mathrm{getting}\:\mathrm{the}\:\mathrm{minimum}\right)\:\mathrm{using}\:\mathrm{backprobagation}? \\ $$$$ \\ $$$$\alpha\left({x}_{{i}} ,{y}_{{i}} ,{h}_{{i}} \right)=\left({h}_{{i}} −{x}_{{i}} \right)^{\mathrm{2}} +{y}_{{i}} ^{\mathrm{2}} \\ $$$$\beta\left({y}_{{i}} ,{h}_{{i}} \right)={y}_{{i}}…
Question Number 61804 by maxmathsup by imad last updated on 09/Jun/19 $${calculate}\:\sum_{{n}=\mathrm{2}} ^{\infty} \:\sum_{{k}=\mathrm{2}} ^{\infty} \:\:\:\frac{\mathrm{1}}{{k}^{{n}} \:\:{k}!} \\ $$ Commented by maxmathsup by imad last…
Question Number 127332 by snipers237 last updated on 28/Dec/20 $${let}\:{a},{b},{c}\:{be}\:{integers}\:{such}\:{as} \\ $$$$\mathrm{0}<{a}^{\mathrm{2}} +{b}^{\mathrm{2}} −{abc}\:<\:{c}\: \\ $$$${prove}\:{that}\:\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} −{abc}}\:\:{is}\:{an}\:{integer} \\ $$ Terms of Service Privacy Policy…
Question Number 61751 by maxmathsup by imad last updated on 08/Jun/19 $${use}\:{newton}\:{method}\:{to}\:{solve}\:{the}\:{equation}\:\:{x}^{\mathrm{4}} −\mathrm{3}{x}−\mathrm{1}\:=\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 61657 by maxmathsup by imad last updated on 05/Jun/19 $${U}_{{n}} \:{and}\:{V}_{{n}} \:\:{are}\:{two}\:{sequences}\:\:{verify}\:\:{U}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:{V}_{{k}} \\ $$$${determine}\:{V}_{{n}} \:\:{interms}\:{of}\:\:{U}_{{k}} \:\:\:\:\:\:\:,\mathrm{0}\leqslant{k}\leqslant{n} \\ $$…
Question Number 61536 by maxmathsup by imad last updated on 04/Jun/19 $$\left.\mathrm{1}\right){let}\:{U}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \left(−\mathrm{1}\right)^{{k}} \:=\mathrm{1}−\mathrm{1}+\mathrm{1}−\mathrm{1}+…\left({n}+\mathrm{1}\:{terms}\right) \\ $$$${is}\:{lim}_{{n}\rightarrow+\infty} {U}_{{n}} {exist}\:?\:\:{find}\:{U}_{{n}} \:{by}\:{using}\:{integr}\:{part}\left[..\right] \\ $$$$\left.\mathrm{2}\right)\:{let}\:{V}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}}…
Question Number 61532 by maxmathsup by imad last updated on 04/Jun/19 $${prove}\:{that}\:\:\:\frac{\left({a}+{b}\right)^{{n}} }{{a}^{{n}} \:+{b}^{{n}} }\:<\mathrm{2}^{{n}−\mathrm{1}} \:\:\:\:\:\forall\:{n}>\mathrm{1}\:\:\:\:\left({n}\:{natural}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 61329 by maxmathsup by imad last updated on 01/Jun/19 $${let}\:{f}\left({x}\right)\:=\frac{{e}^{−{x}} }{\mathrm{1}+{x}}\:{sin}\left(\mathrm{3}{x}\right) \\ $$$$\left.\mathrm{1}\right)\:{dtermine}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$ Commented by maxmathsup by…
Question Number 61261 by Jmasanja last updated on 31/May/19 $${for}\:{polynomial}\:{p}\left({x}\right),{the}\:{value}\:{of}\: \\ $$$${p}\left(\mathrm{3}\right)\:{is}\:−\mathrm{2}.{which}\:{of}\:{the}\:{following}\: \\ $$$${must}\:{be}\:{true}\:{about}\:{p}\left({x}\right)? \\ $$$$\left({a}\right){x}−\mathrm{5}\:{is}\:{the}\:{factor}\:{of}\:{p}\left({x}\right) \\ $$$$\left({b}\right){x}−\mathrm{2}{is}\:{the}\:{factor}\:{of}\:{p}\left({x}\right) \\ $$$$\left({c}\right){x}+\mathrm{2}\:{is}\:{the}\:{factor}\:{of}\:{p}\left({x}\right) \\ $$$$\left({d}\right){the}\:{reminder}\:{when}\:\:{p}\left({x}\right)\:{is}\:{divide} \\ $$$${d}\:{by}\:{x}−\mathrm{3}\:{is}\:−\mathrm{2} \\…