Category: Relation and Functions

Question Number 53778 by maxmathsup by imad last updated on 25/Jan/19 $$let{U}_n=\frac{1}{{nH}_n}with{H}_n=\sum _{k=1}^n\frac{1}{k}$$$$studytheconvergenceof\sum _{n⩾1}{U}_n$$$$\left.\mathrm{2}\right)\:{study}\:{the}\:{convergence}\:{of}\:\sum_{{n}\geqslant\mathrm{1}} {U}_{{n}} ^{\mathrm{2}} \…

Question Number 119214 by abdul88 last updated on 23/Oct/20 $$f\left(x\right)=\left(\underset{0}{\stackrel{1}{\int }}f\left(x\right)dx\right)x^2+\left(\underset{0}{\stackrel{2}{\int }}f\left(x\right)dx\right)x+\left(\underset{0}{\stackrel{3}{\int }}f\left(x\right)dx\right)+1$$$$thevaleuf\left(4\right)=?$$ Answered by bemath last…

Question Number 118960 by bramlexs22 last updated on 21/Oct/20 $$Givenf:R\to Randg:R\to R$$$$wheref\left(x\right)=x^3+3andg\left(x\right)=2x+1.Find$$$$thevalueof{f}^{-1}\left(g^{-1}\left(23\right)\right).$$ Answered by benjo_mathlover last updated on…

Question Number 52682 by maxmathsup by imad last updated on 11/Jan/19 $$findnatureoftheserie\sum _{n=1}^{\mathrm{\infty }}\frac{\sqrt{n+1}-\sqrt{n}}{nln(n+1)}$$ Commented by Abdo msup. last updated on 12/Jan/19 $${let}\:{u}_{{n}}…

Question Number 52677 by maxmathsup by imad last updated on 11/Jan/19 $$findnatureof\sum _{n=2}^{\mathrm{\infty }}{(-1)}^n\sqrt{n}ln\left(\frac{n+1}{n-1}\right).$$ Commented by maxmathsup by imad last updated on…