Category: Relation and Functions

Question Number 111766 by mathmax by abdo last updated on 04/Sep/20 $$\mathrm{calculate}{\lim }_{\mathrm{n}\to +\mathrm{\infty }}\sum _{\mathrm{k}=1}^{\mathrm{n}}\ln {\left(\frac{\mathrm{n}}{\mathrm{n}+\mathrm{k}}\right)}^{\frac{1}{\mathrm{n}}}$$ Answered by Dwaipayan Shikari last updated on 04/Sep/20…

Question Number 111754 by mathmax by abdo last updated on 04/Sep/20 $$$$$$\mathrm{calculate}{\lim }_{\mathrm{n}\to +\mathrm{\infty }}\sum _{\mathrm{k}=1}^{2\mathrm{n}}\frac{\mathrm{k}}{{\mathrm{k}}^2+{\mathrm{n}}^2}$$ Answered by Dwaipayan Shikari…

Question Number 177146 by mathlove last updated on 01/Oct/22 $$f\left(x\right)=f(x-1)+x^2+2x$$$$f\left(6\right)=33faindvolueoff\left(50\right)=?$$ Answered by cortano1 last updated on 01/Oct/22 $$\:\mathrm{f}\left(\mathrm{x}\right)−\mathrm{f}\left(\mathrm{x}−\mathrm{1}\right)=\mathrm{x}^{\mathrm{2}} +\mathrm{2x} \…

Question Number 111535 by Aina Samuel Temidayo last updated on 04/Sep/20 $$\mathrm{If}\mathrm{f}\left(\mathrm{x}\right)={\mathrm{ax}}^2-\mathrm{c}\mathrm{satisfy}-4⩽\mathrm{f}\left(1\right)⩽-1$$$$\mathrm{and}-1⩽\mathrm{f}\left(2\right)⩽5,\mathrm{then}$$$$$$$$\mathrm{A}.7⩽\mathrm{f}\left(3\right)⩽26\mathrm{B}.-1⩽\mathrm{f}\left(3\right)⩽20\mathrm{C}.$$$$-4⩽\mathrm{f}\left(3\right)⩽15\mathrm{D}.\frac{-28}{3}⩽\mathrm{f}\left(3\right)⩽\frac{35}{3}\mathrm{E}.$$$$\frac{8}{3}⩽\mathrm{f}\left(3\right)⩽\frac{13}{3}$$…

Question Number 45968 by maxmathsup by imad last updated on 19/Oct/18 $$1)find\sum _{n=1}^{\mathrm{\infty }}\frac{cos\left(nx\right)}{n}and\sum _{n=1}^{\mathrm{\infty }}\frac{sin\left(nx\right)}{n}$$$$2)calculate\sum _{n=1}^{\mathrm{\infty }}\frac{1}{n}cos\left(\frac{2n\pi }{3}\right)and\sum _{n=1}^{\mathrm{\infty }}\frac{1}{n}sin\left(\frac{2n\pi }{3}\right)$$ Commented…