Category: Relation and Functions

Question Number 33708 by math khazana by abdo last updated on 22/Apr/18 $$find\sum _{n=0}^{\mathrm{\infty }}(n+1)x^{3n}$$$$2)calculate\sum _{n=0}^{\mathrm{\infty }}\frac{n+1}{8^n}.$$ Terms of Service…

Question Number 33707 by math khazana by abdo last updated on 22/Apr/18 $$findtheradiusofconvergencefor$$$$\sum _{n⩾2}\left({\int }_{n-\frac{1}{2}}^{n+\frac{1}{2}}\frac{dx}{\sqrt{x^3+x+1}}\right)x^n.$$ Terms of Service…

Question Number 99240 by abdomathmax last updated on 19/Jun/20 $$\mathrm{let}\mathrm{f}\left(\mathrm{x}\right)=\sqrt{1+\mathrm{cosx}}\mathrm{developp}\mathrm{f}\mathrm{at}\mathrm{fourier}\mathrm{serie}$$ 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 33701 by math khazana by abdo last updated on 22/Apr/18 $$let\mathrm{\Sigma }{f}_n\left(x\right)with{f}_n\left(x\right)=\frac{sin\left(nx\right)}{n^2(n+1)}andSitssum$$$$x\in [-\pi ,\pi ]provethat\mathrm{\forall }(x,y)\in {[-\pi ,\pi ]}^2$$$$x\ne y\Rightarrow \mid S\left(x\right)-S\left(y\right)\mid <\mid x-y\mid .$$ Terms of Service…

Question Number 99237 by abdomathmax last updated on 19/Jun/20 $$\mathrm{calculate}{\lim }_{\mathrm{n}\to +\mathrm{\infty }}\sum _{\mathrm{k}=1}^{\mathrm{n}}\frac{\sqrt{\mathrm{kn}}}{({\mathrm{k}}^2+{\mathrm{n}}^2)}$$ Answered by Ar Brandon last updated on 19/Jun/20…