Category: Relation and Functions

Question Number 40046 by abdo mathsup 649 cc last updated on 15/Jul/18 $$let{S}_n=\sum _{k=2}^n\frac{{(-1)}^k}{k^2-1}$$$$1)calculate{S}_{n}intermsof{H}_n$$$$\left(\:{H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}}…

Question Number 105566 by mathmax by abdo last updated on 30/Jul/20 $$\mathrm{let}\mathrm{f}\left(\mathrm{x}\right)={(\mathrm{x}+1)}^{2\mathrm{n}}{\mathrm{e}}^{-\mathrm{x}}\sin \left(\mathrm{x}\right)$$$$1)\mathrm{calculate}{\mathrm{f}}^{\left(\mathrm{n}\right)}\left(\mathrm{x}\right)\mathrm{and}{\mathrm{f}}^{\left(\mathrm{n}\right)}\left(0\right)$$$$2)\mathrm{developp}\mathrm{f}\mathrm{at}\mathrm{integr}\mathrm{serie}$$$$3)\mathrm{find}\int \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}$$ Terms…

Question Number 39891 by math khazana by abdo last updated on 13/Jul/18 $$letf\left(x\right)=arctan(2x+1)$$$$1)calculate{f}^{\left(n\right)}\left(x\right)$$$$2)calculate{f}^{\left(n\right)}\left(0\right)$$$$3)developpfatintegrserie$$$$\left.\mathrm{4}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:{f}\left({x}\right){dx}…

Question Number 39837 by math khazana by abdo last updated on 12/Jul/18 $$let{S}_n=\sum _{n=1}^{\mathrm{\infty }}{e}^{-n\left[\frac{x}{n}\right]}$$$$findaequivalentof{S}_{n}whenn\to +\mathrm{\infty }$$ Terms of Service Privacy…

Question Number 39703 by math khazana by abdo last updated on 10/Jul/18 $$let{A}_n={\int }_0^n\frac{{(-1)}^{\left[x\right]}}{x+2-\left[x\right]}dx$$$$1)calculate{A}_{n}and{lim}_{n\to +\mathrm{\infty }}{A}_n$$$$\left.\mathrm{2}\right)\:{let}\:{S}_{{n}} \:=\sum_{{n}=\mathrm{0}}…