Category: Relation and Functions

Question Number 36927 by maxmathsup by imad last updated on 07/Jun/18 $$fisarealfunctionderivableon[0,1]/f\left(0\right)=0andf\left(1\right)=1$$$$provethat\mathrm{\forall }n\in N\mathrm{\exists }{\left(x_i\right)}_{1⩽i⩽n}seqenceofrealswith{x}_i\ne x_{j}ifi\ne j$$$${and}\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{f}^{'} \left({x}_{{k}} \right)={n}. \…

Question Number 36922 by maxmathsup by imad last updated on 07/Jun/18 $$\left(u_n\right)isasequenceand{lim}_{n\to +\mathrm{\infty }}{u}_n=llet$$$${v}_{{n}} =\:\frac{\mathrm{1}}{\mathrm{2}^{{n}} }\:\sum_{{k}=\mathrm{0}} ^{{n}} {C}_{{n}} ^{{k}} \:{u}_{{k}} \:\:{prove}\:{that}\:{v}_{{n}} \:\rightarrow{l}\left({n}\rightarrow+\infty\:\right)…

Question Number 36924 by maxmathsup by imad last updated on 07/Jun/18 $$calculate{lim}_{n\to +\mathrm{\infty }}\frac{1}{2i}\{{(1+\frac{it}{n})}^n-{(1-\frac{it}{n})}^n)$$ Commented by math khazana by abdo last updated…

Question Number 36920 by maxmathsup by imad last updated on 07/Jun/18 $$let\alpha fromRand{u}_n-2cos\left(\alpha \right)u_{n-1}+u_{n-2}=0withn⩾2$$$$find{u}_{n}andstudyitsconvrgence.$$ Commented by math khazana by…

Question Number 36820 by maxmathsup by imad last updated on 06/Jun/18 $$findthevalueof\sum _{n=2}^{\mathrm{\infty }}\frac{1}{{(n-1)}^2{(n+1)}^2}$$ Commented by math khazana by abdo last…