Category: Relation and Functions

Question Number 129869 by Bird last updated on 20/Jan/21 $$calculate{lim}_{n\to +\mathrm{\infty }}\sum _{k=1}^n\frac{1}{\sqrt{(k+n)(k+1+n})}$$ Answered by mindispower last updated on 20/Jan/21 $$$$$$\frac{\mathrm{1}}{\left({k}+\mathrm{1}+{n}\right)}\leqslant\frac{\mathrm{1}}{\:\sqrt{{k}+{n}}.\sqrt{{k}+\mathrm{1}+{n}}}\leqslant\frac{\mathrm{1}}{{k}+{n}}…\mathrm{1}…

Question Number 129403 by bemath last updated on 15/Jan/21 $$\mathrm{f}\left(\mathrm{n}\right)=4\mathrm{f}(\mathrm{n}-1)-4\mathrm{f}(\mathrm{n}-2)+{\mathrm{n}}^2$$$$\mathrm{and}\mathrm{f}\left(0\right)=2,\mathrm{f}\left(1\right)=5$$ Commented by talminator2856791 last updated on 15/Jan/21 $$\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{question}?$$…

Question Number 129336 by bramlexs22 last updated on 15/Jan/21 $$\mathrm{If}a,b\mathrm{and}c\mathrm{are}\mathrm{the}\mathrm{roots}\mathrm{of}$$$$x^3-21x-35=0\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{value}\mathrm{of}$$$$(a-b)(c-a)(b-c)?$$ Commented by MJS_new last updated on 22/Jan/21 $${x}^{\mathrm{3}}…

Question Number 63665 by mathmax by abdo last updated on 07/Jul/19 $$findthevalueof\sum _{n=1}^{\mathrm{\infty }}\frac{{(-1)}^n}{n^2{(n+1)}^3}$$ Commented by mathmax by abdo last…

Question Number 63560 by mathmax by abdo last updated on 05/Jul/19 $$developpatlaurentseries$$$$1)f\left(z\right)=\frac{1}{z-2}$$$$2)g\left(z\right)=\frac{3}{z^2-3z+2}$$$$3)h\left(z\right)=\frac{1}{z^2+4}$$ Commented by mathmax…