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Category: Relation and Functions

1-find-the-radius-of-convergence-for-n-1-x-n-n-n-1-n-2-and-calculate-its-sum-2-find-the-value-of-n-1-1-n-n-2-n-n-1-n-2-

Question Number 33710 by math khazana by abdo last updated on 22/Apr/18 $$\left.\mathrm{1}\right)\:{find}\:{the}\:{radius}\:{of}\:{convergence}?{for} \\ $$$$\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{{x}^{{n}} }{{n}\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)}\:{and}\:{calculate}\:{its}\:{sum} \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}\:\mathrm{2}^{{n}}…

find-the-radius-of-convergence-for-n-2-n-1-2-n-1-2-dx-x-3-x-1-x-n-

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…

let-f-x-1-cosx-developp-f-at-fourier-serie-

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}}…

let-f-n-x-with-f-n-x-sin-nx-n-2-n-1-and-S-its-sum-x-pi-pi-prove-that-x-y-pi-pi-2-x-y-S-x-S-y-lt-x-y-

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…