Category: Relation and Functions

Question Number 33131 by prof Abdo imad last updated on 11/Apr/18 $$1)find\sum _{n=1}^{\mathrm{\infty }}\frac{e^{inx}}{n(n+1)}$$$$2)findthevalueof\sum _{n⩾1}\frac{sin\left(nx\right)}{n(n+1)}$$$$and\sum _{n⩾1}\frac{cos\left(nx\right)}{n(n+1)}.$$ Commented by…

Question Number 33126 by prof Abdo imad last updated on 10/Apr/18 $$letgivef\left(x\right)=\frac{1}{2x^2-3x+1}$$$$1)find{f}^{\left(n\right)}\left(x\right)$$$$2)find{f}^{\left(n\right)}\left(0\right)$$$$3)iff\left(x\right)=\mathrm{\Sigma }{a}_n{x}^{n}calculatethesequence{a}_n$$…

Question Number 98657 by mathmax by abdo last updated on 15/Jun/20 $$\mathrm{solve}{\mathrm{y}}^{{}^{″}}-{3\mathrm{y}}^{{}^{\prime }}+2\mathrm{y}=\frac{\mathrm{sinx}}{\mathrm{x}}$$ Answered by maths mind last updated on 15/Jun/20 $${y}''−\mathrm{3}{y}'+\mathrm{2}{y}=\mathrm{0}…

Question Number 164176 by mathlove last updated on 15/Jan/22 Answered by mr W last updated on 15/Jan/22 $$f\left(x\right)+f\left(\frac{1}{1-x}\right)=x\dots \left(i\right)$$$$replacexwith1-\frac{1}{x}$$$$\Rightarrow f\left(\frac{x-1}{x}\right)+f\left(x\right)=1-\frac{1}{x}\dots \left(ii\right)$$$${replace}\:{x}\:{with}\:\frac{\mathrm{1}}{\mathrm{1}−{x}} \…

Question Number 33074 by prof Abdo imad last updated on 10/Apr/18 $$findintermsofnthesum\sum _{k=0}^n{k}^2{C}_n^k$$ Commented by abdo imad last updated on…