Category: Relation and Functions

Question Number 67533 by mathmax by abdo last updated on 28/Aug/19 $$findthevalueof\prod _{n=1}^{\mathrm{\infty }}(1+\frac{1}{n(n+2)})$$$$\prod _{n=1}^{\mathrm{\infty }}(1-\frac{2}{n(n+1)})$$ Terms of Service Privacy Policy…

Question Number 67522 by mathmax by abdo last updated on 28/Aug/19 $$letzfromC-Zprovethat$$$$\frac{\pi }{sin\left(\pi z\right)}=\frac{1}{z}+\sum _{n=1}^{\mathrm{\infty }}\frac{{(-1)}^{n}2z}{z^2-n^2}and$$$$\frac{\pi{cos}\left(\pi{z}\right)}{{sin}\left(\pi{z}\right)}\:=\frac{\mathrm{1}}{{z}}\:+\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{2}{z}}{{z}^{\mathrm{2}} −{n}^{\mathrm{2}} }…

Question Number 67521 by mathmax by abdo last updated on 28/Aug/19 $$calculateA\left(x\right)=\sum _{n=1}^{\mathrm{\infty }}\frac{{(-1)}^{n}cos\left(nx\right)}{n}$$$$andB\left(x\right)=\sum _{n=1}^{\mathrm{\infty }}\frac{{(-1)}^{n}sin\left(nx\right)}{n}$$ Terms of Service…

Question Number 67519 by mathmax by abdo last updated on 28/Aug/19 $$if\frac{z}{e^z-1}=\sum _{n=0}^{\mathrm{\infty }}{B}_n\frac{z^n}{n!}$$$$1)calculate{B}_0,B_1,B_2,B_3,B_4$$$$\left.\mathrm{2}\right){prove}\:{that}\:{z}\rightarrow\frac{\mathrm{1}}{{e}^{{z}}…

Question Number 1976 by 123456 last updated on 27/Oct/15 $$f:\mathbb{R}\to \mathbb{R}$$$$g:\mathbb{R}\to \mathbb{R}$$$$f(x+y)=f\left(x\right)g\left(x\right)+f\left(y\right)g\left(y\right)$$$$g(x+y)=f\left(x\right)f\left(y\right)+g\left(x\right)g\left(y\right)$$$${\left[f\left(x\right)\right]}^2+{\left[g\left(x\right)\right]}^2=?$$$$[f\left(x\right)+g\left(y\right)][g\left(x\right)+f\left(y\right)]=??$$$${f}\left({x}\right)=??? \…