Question Number 32277 by abdo imad last updated on 22/Mar/18 $${for}\:{x}_{{i}} \:\in\left[\mathrm{0},\mathrm{1}\right]\:{prove}\:{that} \\ $$$$\left(\mathrm{1}−{x}_{\mathrm{1}} \right)\left(\mathrm{1}−{x}_{\mathrm{2}} \right)….\left(\mathrm{1}−{x}_{{n}} \right)\:\geqslant\mathrm{1}−\left({x}_{\mathrm{1}} +{x}_{\mathrm{2}} \:+….\:+{x}_{{n}} \right). \\ $$ Terms of Service…
Question Number 32274 by abdo imad last updated on 22/Mar/18 $${prove}\:{that}\:\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\:\frac{\mathrm{2}^{{k}} }{{x}^{\mathrm{2}^{{k}} } \:+\mathrm{1}}\:=\:\frac{\mathrm{1}}{{x}−\mathrm{1}}\:−\:\frac{\mathrm{2}^{{n}+\mathrm{1}} }{{x}^{\mathrm{2}^{{n}+\mathrm{1}} \:} −\mathrm{1}}\:\:. \\ $$ Terms of Service Privacy…
Question Number 32273 by abdo imad last updated on 22/Mar/18 $${let}\:{put}\:{u}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:{k}\left({k}!\right) \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{u}_{{n}} =\left({n}+\mathrm{1}\right)!\:−\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{study}\:{the}\:{convergence}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{{u}_{{n}} }\:. \\ $$ Commented…
Question Number 32271 by abdo imad last updated on 22/Mar/18 $${study}\:{the}\:{convergence}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} }{{n}^{\frac{\mathrm{1}}{\mathrm{3}}} }\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 97799 by abdomathmax last updated on 09/Jun/20 $$\mathrm{solve}\:\mathrm{y}^{'} \mathrm{cosx}\:+\mathrm{y}\:\mathrm{sinx}\:=\mathrm{cosx}\:+\mathrm{sinx} \\ $$ Commented by john santu last updated on 10/Jun/20 $$\frac{{dy}}{{dx}}\:+\:\mathrm{tan}\:{x}\:.{y}\:=\:\mathrm{1}+\mathrm{tan}\:{x} \\ $$$$\mathrm{IF}\:{u}\left({x}\right)={e}^{\int\:\mathrm{tan}\:{x}\:{dx}} \:=\:{e}^{\mathrm{ln}\left(\mathrm{sec}\:{x}\right)}…
Question Number 97798 by abdomathmax last updated on 09/Jun/20 $$\mathrm{solve}\:\mathrm{y}''−\mathrm{y}\:=\mathrm{xsin}\left(\mathrm{2x}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 97797 by abdomathmax last updated on 09/Jun/20 $$\mathrm{solve}\:\mathrm{y}^{''} \:−\mathrm{y}\:=\:\mathrm{x} \\ $$ Answered by niroj last updated on 09/Jun/20 $$\:\mathrm{y}^{''} −\mathrm{y}\:=\:\mathrm{x} \\ $$$$\:\:\left(\mathrm{D}^{\mathrm{2}} −\mathrm{1}\right)\mathrm{y}=\:\mathrm{x}…
Question Number 97795 by abdomathmax last updated on 09/Jun/20 $$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}−\mathrm{1}} }{\left[\sqrt{\mathrm{n}}\right]} \\ $$$$\left[..\right]\:\mathrm{meant}\:\mathrm{the}\:\mathrm{floor} \\ $$ Answered by bobhans last updated on 10/Jun/20 $$\lfloor\sqrt{\mathrm{n}}\:\rfloor\:=\:\mathrm{m}\:\in\mathbb{N}…
Question Number 97648 by bobhans last updated on 09/Jun/20 $$\mathrm{Determine}\:\mathrm{all}\:\mathrm{function}\:\mathrm{f}:\mathrm{R}/\left\{\mathrm{0},\mathrm{1}\right\}\rightarrow\mathrm{R} \\ $$$$\mathrm{satisfying}\:\mathrm{the}\:\mathrm{functional}\:\mathrm{relation} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:+\:\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{1}−\mathrm{x}}\right)\:=\:\frac{\mathrm{2}\left(\mathrm{1}−\mathrm{2x}\right)}{\mathrm{x}\left(\mathrm{1}−\mathrm{x}\right)}\:,\:\mathrm{x}\neq\mathrm{0},\:\mathrm{x}\neq\mathrm{1} \\ $$ Commented by bemath last updated on 09/Jun/20 $$\mathrm{nice}\:\mathrm{question} \\…
Question Number 97626 by mathmax by abdo last updated on 08/Jun/20 $$\mathrm{solve}\:\mathrm{y}^{''} \:−\mathrm{2y}^{'} \:+\mathrm{y}\:\:=\mathrm{x}^{\mathrm{2}} \:\mathrm{with}\:\mathrm{y}^{'} \left(\mathrm{0}\right)\:=\mathrm{y}\left(\mathrm{0}\right)\:=−\mathrm{1} \\ $$ Commented by bemath last updated on 09/Jun/20…