Question Number 40047 by abdo mathsup 649 cc last updated on 15/Jul/18 $${let}\:{S}_{{n}} \:=\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\frac{\left(−\mathrm{1}\right)^{{k}} }{\mathrm{2}{k}+\mathrm{1}} \\ $$$$\left.\mathrm{1}\right)\:{give}\:{S}_{{n}} \:{interms}\:{of}\:{H}_{{n}} \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{n}\rightarrow+\infty} {S}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{let}\:{W}_{{n}}…
Question Number 40046 by abdo mathsup 649 cc last updated on 15/Jul/18 $${let}\:{S}_{{n}} =\:\sum_{{k}=\mathrm{2}} ^{{n}} \:\:\frac{\left(−\mathrm{1}\right)^{{k}} }{{k}^{\mathrm{2}} −\mathrm{1}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\:{S}_{{n}} \:\:{interms}\:{of}\:{H}_{{n}} \\ $$$$\left(\:{H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}}…
Question Number 40040 by abdo mathsup 649 cc last updated on 15/Jul/18 $${let}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{{n}} \:\:{e}^{−{n}\left(\:{x}+\mathrm{2}−\left[{x}\right]\right)} {dx}\:\:{with}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{study}\:{the}\:{convergence}\:{of}\:\:\:\sum_{{n}} {A}_{{n}}…
Question Number 105566 by mathmax by abdo last updated on 30/Jul/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2n}} \:\mathrm{e}^{−\mathrm{x}} \mathrm{sin}\left(\mathrm{x}\right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \:\left(\mathrm{x}\right)\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{find}\:\int\:\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx} \\ $$ Terms…
Question Number 39892 by math khazana by abdo last updated on 13/Jul/18 $${let}\:{g}\left({x}\right)=\:{e}^{−\mathrm{2}{x}} \:{arctan}\left({x}+\mathrm{3}\right) \\ $$$${developp}\:{g}\:{at}\:{integr}\:{serie}\:\:. \\ $$ Commented by math khazana by abdo last…
Question Number 39891 by math khazana by abdo last updated on 13/Jul/18 $${let}\:{f}\left({x}\right)={arctan}\left(\mathrm{2}{x}+\mathrm{1}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:{f}\left({x}\right){dx}…
Question Number 39839 by math khazana by abdo last updated on 12/Jul/18 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{1}} \:\:\:\int_{{x}} ^{{x}^{\mathrm{2}} } \:\:\:\frac{{arctan}\left(\mathrm{2}{t}\right)}{{sin}\left(\pi{t}\right)}{dt} \\ $$ Commented by math khazana by abdo…
Question Number 39837 by math khazana by abdo last updated on 12/Jul/18 $${let}\:{S}_{{n}} =\sum_{{n}=\mathrm{1}} ^{\infty} \:\:{e}^{−{n}\left[\frac{{x}}{{n}}\right]} \\ $$$${find}\:{a}\:{equivalent}\:{of}\:{S}_{{n}} \:{when}\:{n}\rightarrow+\infty \\ $$ Terms of Service Privacy…
Question Number 39835 by math khazana by abdo last updated on 12/Jul/18 $${simplify}\:\left[\frac{\left[{nx}\right]}{{n}}\right]\:{with}\:{n}\:{natural}\:{integr}\:{not}\mathrm{0}\:\:{and}\:{x}\:{real} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 39703 by math khazana by abdo last updated on 10/Jul/18 $${let}\:\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{{n}} \:\:\:\frac{\left(−\mathrm{1}\right)^{\left[{x}\right]} }{{x}+\mathrm{2}−\left[{x}\right]}{dx} \\ $$$$\left.\mathrm{1}\right)\:\:{calculate}\:{A}_{{n}} \:\:\:{and}\:{lim}_{{n}\rightarrow+\infty} \:\:{A}_{{n}} \: \\ $$$$\left.\mathrm{2}\right)\:{let}\:{S}_{{n}} \:=\sum_{{n}=\mathrm{0}}…