Category: Relation and Functions

Question Number 33890 by math khazana by abdo last updated on 26/Apr/18 $$find{lim}_{x\to +\mathrm{\infty }}\sum _{n=1}^{\mathrm{\infty }}{(1+\frac{1}{n})}^{n^2}\frac{x^n}{n!}.$$ Terms of Service Privacy…

Question Number 33892 by math khazana by abdo last updated on 26/Apr/18 $$provethat\sum _{n=1}^{\mathrm{\infty }}\frac{H_n}{n^2}=2\xi \left(3\right)with$$$$\xi \left(x\right)=\sum _{n=1}^{\mathrm{\infty }}\frac{1}{n^x}andx>1.$$ Commented…

Question Number 33887 by math khazana by abdo last updated on 26/Apr/18 $$findthevalueof\sum _{n=0}^{\mathrm{\infty }}\frac{{(-1)}^n}{4n+1}.$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 33848 by prof Abdo imad last updated on 26/Apr/18 $$let{w}_n=\frac{H_n^2}{n}with{H}_n=\sum _{k=1}^n\frac{1}{k}$$$${study}\:{the}\:{convergence}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:{w}_{{n}} {x}^{{n}} \:\:. \…

Question Number 33847 by prof Abdo imad last updated on 26/Apr/18 $$letgiveasequenceofrealnumbetspositif$$$${\left(a_i\right)}_{1⩽i⩽n}$$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\left(\sum_{{i}=\mathrm{1}} ^{{n}} \:{a}_{{i}} \right)^{\mathrm{2}} \leqslant\:{n}\:\sum_{{i}=\mathrm{1}} ^{{n}} \:{a}_{{i}} ^{\mathrm{2}} \…