Question Number 33708 by math khazana by abdo last updated on 22/Apr/18 $${find}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\left({n}+\mathrm{1}\right){x}^{\mathrm{3}{n}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\:\frac{{n}+\mathrm{1}}{\mathrm{8}^{{n}} }\:. \\ $$ Terms of Service…
Question Number 33709 by math khazana by abdo last updated on 22/Apr/18 $${find}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\left({n}+\mathrm{1}\right){x}^{\mathrm{3}{n}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\:\frac{{n}+\mathrm{1}}{\mathrm{8}^{{n}} }\:. \\ $$ Commented by prof…
Question Number 33707 by math khazana by abdo last updated on 22/Apr/18 $${find}\:{the}\:{radius}\:{of}\:{convergence}\:{for} \\ $$$$\sum_{{n}\geqslant\mathrm{2}} \left(\:\int_{{n}−\frac{\mathrm{1}}{\mathrm{2}}} ^{{n}+\frac{\mathrm{1}}{\mathrm{2}}} \:\:\:\:\frac{{dx}}{\:\sqrt{{x}^{\mathrm{3}} +{x}\:+\mathrm{1}}}\right){x}^{{n}} \:\:. \\ $$ Terms of Service…
Question Number 99242 by abdomathmax last updated on 19/Jun/20 $$\mathrm{calculate}\:\mathrm{L}\left(\mathrm{e}^{−\mathrm{ax}} \:\mathrm{ch}\left(\mathrm{3x}\right)\right)\:\:\mathrm{with}\:\mathrm{a}>\mathrm{0} \\ $$ Commented by PRITHWISH SEN 2 last updated on 20/Jun/20 $$\int_{\mathrm{0}} ^{\infty} \mathrm{e}^{−\left(\mathrm{s}+\mathrm{a}\right)\mathrm{x}}…
Question Number 99240 by abdomathmax last updated on 19/Jun/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\sqrt{\mathrm{1}+\mathrm{cosx}}\:\:\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$ Answered by mathmax by abdo last updated on 20/Jun/20 $$\mathrm{f}\left(\mathrm{x}\right)\:=\sqrt{\mathrm{1}+\mathrm{cosx}}\:\:\:\mathrm{f}\:\mathrm{is}\:\mathrm{even}\:\mathrm{2}\pi\:\mathrm{periodic}\:\Rightarrow\mathrm{f}\left(\mathrm{x}\right)\:=\frac{\mathrm{a}_{\mathrm{0}} }{\mathrm{2}}\:+\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\mathrm{a}_{\mathrm{n}}…
Question Number 99241 by abdomathmax last updated on 19/Jun/20 $$\mathrm{let}\:\mathrm{g}\left(\mathrm{x}\right)=\sqrt{\mathrm{1}−\mathrm{cosx}}\:\mathrm{developp}\:\mathrm{g}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 33701 by math khazana by abdo last updated on 22/Apr/18 $${let}\:\Sigma\:{f}_{{n}} \left({x}\right)\:{with}\:{f}_{{n}} \left({x}\right)\:=\:\frac{{sin}\left({nx}\right)}{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)}\:\:{and}\:{S}\:{its}\:{sum} \\ $$$${x}\in\left[−\pi,\pi\right]\:{prove}\:{that}\:\forall\left({x},{y}\right)\in\left[−\pi,\pi\right]^{\mathrm{2}} \\ $$$${x}\neq{y}\:\Rightarrow\mid{S}\left({x}\right)−{S}\left({y}\right)\mid<\mid{x}−{y}\mid\:. \\ $$ Terms of Service…
Question Number 99236 by abdomathmax last updated on 19/Jun/20 $$\mathrm{find}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}} \:\frac{\mathrm{k}}{\mathrm{n}}\mathrm{e}^{−\frac{\mathrm{k}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} }} \\ $$ Commented by Ar Brandon last updated on 19/Jun/20…
Question Number 99237 by abdomathmax last updated on 19/Jun/20 $$\mathrm{calculate}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\:\:\:\:\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}} \:\:\frac{\sqrt{\mathrm{kn}}}{\left(\mathrm{k}^{\mathrm{2}} \:+\mathrm{n}^{\mathrm{2}} \right)} \\ $$ Answered by Ar Brandon last updated on 19/Jun/20…
Question Number 33698 by math khazana by abdo last updated on 22/Apr/18 $${let}\:\:{f}_{{n}} \left({x}\right)=\:{n}^{{x}} \:{e}^{−{nx}} \:\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{study}\:{the}\:{simple}\:{and}\:{uniform}\:{convervence}\:{for} \\ $$$$\Sigma\:\:{f}_{{n}} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{let}\:\:{S}\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\infty} \:{f}_{{n}}…