Question Number 3685 by Filup last updated on 19/Dec/15 $$\mathrm{let}\:{p}_{{i}} \:\mathrm{be}\:\mathrm{the}\:{i}^{\mathrm{th}} \:\mathrm{prime} \\ $$$$ \\ $$$$\mathrm{Does}\:\mathrm{the}\:\mathrm{fillowing}\:\mathrm{sum}\:\mathrm{converge}: \\ $$$$\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{p}_{{i}} }{{p}_{{i}+\mathrm{1}} } \\ $$$$\left({p}_{\mathrm{1}} =\mathrm{2},\:{p}_{\mathrm{2}}…
Question Number 134758 by rs4089 last updated on 07/Mar/21 Commented by rs4089 last updated on 07/Mar/21 $${prove}\:{it} \\ $$ Answered by mnjuly1970 last updated on…
Question Number 134753 by mathocean1 last updated on 06/Mar/21 $${f}\:{is}\:{defined}\:{in}\:\left[\mathrm{0};\:+\infty\left[.\right.\right. \\ $$$$\begin{cases}{\:}\\{}\\{{f}\left(\mathrm{0}\right)={ln}\mathrm{2}}\end{cases}{f}\left({x}\right)=\int_{{x}} ^{\mathrm{2}{x}} \:\frac{{e}^{−{t}} }{{t}}{dt}\:\:{for}\:{x}>\mathrm{0} \\ $$$$ \\ $$$$\left.\mathrm{1}\right)\:{Given}\:\mathrm{0}\leqslant{f}\left({x}\leqslant\frac{{e}^{−{x}} −{e}^{−\mathrm{2}{x}} }{{x}}.\right. \\ $$$${Calcule}\:{the}\:{lim}\:{f}\left({x}\right)\:{at}\:\mathrm{0}\:{and}\:+\infty. \\ $$$$\left.\mathrm{2}\right)\:{Calculate}\:{f}\:'\left({x}\right)\:,\:{give}\:{its}\:{variation}…
Question Number 134752 by mathocean1 last updated on 06/Mar/21 $${In}\:{a}\:{locality},\:\mathrm{20\%}\:{of}\:{population}\:{have} \\ $$$${a}\:{chronic}\:{disease}.\:{Among}\:{these}\: \\ $$$${people}\:{who}\:{has}\:{a}\:{chronic}\:{disease},\:\mathrm{2}.\mathrm{5}\:\% \\ $$$${have}\:{COVID}−\mathrm{19}.\:{Among}\:{the}\:{people} \\ $$$${who}\:{don}'{t}\:{have}\:{a}\:{chronic}\:{disease},\:\mathrm{99\%} \\ $$$${have}\:{not}\:{COVID}−\mathrm{19}. \\ $$$$\boldsymbol{{C}}{alculate}\:{the}\:{probability}\:{that}\:{one}\:{person} \\ $$$${of}\:{this}\:{locality}\:{has}\:{COVID}−\mathrm{19}\:{and}\:{a} \\…
Question Number 3682 by Yozzii last updated on 19/Dec/15 $$\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{r}\mathrm{2}^{{r}} }=? \\ $$ Commented by RasheedSindhi last updated on 19/Dec/15 $$\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{r}\mathrm{2}^{{r}}…
Question Number 134751 by mathocean1 last updated on 06/Mar/21 $$\:{In}\:{my}\:{house},\:{there}\:{is}\:\mathrm{250}\:{laptops}:\: \\ $$$$\mathrm{40}\:{are}\:{new},\:\mathrm{100}\:{are}\:{recent}\:{and}\:{the}\: \\ $$$${others}\:{are}\:{old}.\:{A}\:{statistic}\:{showed}\:{that} \\ $$$$\mathrm{4\%}\:{of}\:{new}\:{laptops}\:{are}\:{faulty},\:\mathrm{12\%}\:{of} \\ $$$${recent}\:{ones}\:{are}\:{faulty}\:{and}\:\mathrm{25\%}\:{of}\:{old} \\ $$$${ones}\:{are}\:{faulty}. \\ $$$${Calculate}\:{the}\:{probability}\:{that}\:\mathrm{1}\:{laptop}\:{be} \\ $$$${new}\:,\:{knowing}\:{that}\:{it}\:{is}\:{faulty}. \\…
Question Number 69212 by aliesam last updated on 21/Sep/19 $${use}\:{limit}\:{comparison}\:{test}\:{to}\:{determine} \\ $$$${the}\:{series}\:{converge}\:{or}\:{diverge} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{{k}^{\mathrm{2}} }\right) \\ $$ Answered by mind is power last…
Question Number 134750 by mnjuly1970 last updated on 06/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…..{advanced}\:\:\:{calculus}…. \\ $$$$\:\:\:{prove}\:\:\:{that}::\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\Sigma\frac{\mathrm{1}}{{n}^{\mathrm{3}} {sin}\left(\sqrt{\mathrm{2}}\:\pi{n}\right)}\:=\frac{−\mathrm{13}\sqrt{\mathrm{2}}\:\pi^{\mathrm{3}} \:}{\mathrm{720}} \\ $$$$\:\:\:\:\:…{m}.{n}… \\ $$ Terms of Service Privacy Policy…
Question Number 69211 by Mikael last updated on 21/Sep/19 $${To}\:{conserve}\:{rice}\:{from}\:{a}\:{cooperative}\:{there}\:{is} \\ $$$${a}\:{foil}\:{of}\:{area}\:{A}=\mathrm{24}{cm}^{\mathrm{2}} .\:{The}\:{cooperatives} \\ $$$${want}\:{to}\:{build}\:{a}\:{barn}\:{in}\:{the}\:{shape}\:{of}\:{a}\:{parallelopiped} \\ $$$${square}\:{rectangle}\:{without}\:{cover}. \\ $$$${What}\:{should}\:{be}\:{the}\:{symmetrical}\:{dimensions}\:{for} \\ $$$${the}\:{volume}\:{to}\:{be}\:{maximum}? \\ $$ Terms of…
Question Number 134746 by zahaku last updated on 06/Mar/21 $${How}\:{to}\:{calculate} \\ $$$${li}\underset{{x}\rightarrow−\mathrm{3}} {{m}}\frac{{x}+\mathrm{3}}{\:\sqrt{\mid{x}^{\mathrm{2}} +{x}−\mathrm{6}\mid}}\:\:\:\:? \\ $$ Answered by mathmax by abdo last updated on 06/Mar/21…