Category: Relation and Functions

Question Number 31521 by abdo imad last updated on 09/Mar/18 $$studytheconvergenceof{u}_n=\sqrt{n+1}-\sqrt{n-1}$$ Commented by abdo imad last updated on 12/Mar/18 $${we}\:{have}\:{u}_{{n}} =\sqrt{{n}}\left(\:\sqrt{\mathrm{1}+\frac{\mathrm{1}}{{n}}}\:−\sqrt{\mathrm{1}−\frac{\mathrm{1}}{{n}}}\:\right)\:{but} \…

Question Number 31510 by abdo imad last updated on 09/Mar/18 $$find{lim}_{n\to \mathrm{\infty }}{}^n\sqrt{\prod _{k=1}^n(1+\frac{k}{n^2}})$$ Commented by abdo imad last updated on…

Question Number 31500 by abdo imad last updated on 09/Mar/18 $$let{L}_n\left(x\right)=e^x{\left(e^{-x}{x}^n\right)}^{\left(n\right)}$$$$1)provethat{L}_{n}isapolynomial$$$$2)find{degL}_{n}andtheleadingcoefficient.$$ Commented…

Question Number 31422 by abdo imad last updated on 08/Mar/18 $$find\sum _{n=1}^{\mathrm{\infty }}arctan\left(\frac{2}{16n^2+8n-2}\right).$$ Commented by rahul 19 last updated on 08/Mar/18 $${can}\:{u}\:{plz}\:{provide}\:{sol}.\:{for}\:{this}\:{one}\:.…

Question Number 31417 by abdo imad last updated on 08/Mar/18 $$letgive{u}_n=\sum _{k=1}^n\frac{1}{k}-ln\left(n\right)$$$$1)provethat{u}_{n}isconvergent$$$$2)if\gamma ={lim}_{n\to \mathrm{\infty }}{u}_{n}provethe0<\gamma <1.$$ Terms of…