Category: Relation and Functions

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…

Question Number 45961 by maxmathsup by imad last updated on 19/Oct/18 $$let{f}_n\left(x\right)={(-1)}^{n}ln(1+\frac{x^2}{n(1+x^2)})andf\left(x\right)=\mathrm{\Sigma }{f}_n\left(x\right)$$$$find{lim}_{x\to +\mathrm{\infty }}f\left(x\right).$$ Terms of Service…

Question Number 45960 by maxmathsup by imad last updated on 19/Oct/18 $$findf\left(x\right)=\sum _{n=1}^{\mathrm{\infty }}\frac{x^{n}sin\left(nx\right)}{n}$$ Answered by Smail last updated on 22/Oct/18 $${f}\left({x}\right)={Im}\left(\underset{{n}=\mathrm{1}}…

Question Number 45792 by maxmathsup by imad last updated on 16/Oct/18 $$let{u}_n=\sum _{k=1}^n\frac{{(-1)}^{\left[k\right]}}{k}and{H}_n=\sum _{k=1}^n\frac{1}{k}$$$$1)calculate{u}_{n}intermsof{H}_n$$$$\left.\mathrm{2}\right){study}\:{the}\:{convergence}\:{of}\:\left({u}_{{n}} \right)…

Question Number 45599 by maxmathsup by imad last updated on 14/Oct/18 $$1)calculate{A}_n={\int }_0^n\frac{{(-1)}^{\left[x\right]}}{2x+1-\left[x\right]}dx$$$$2)find{lim}_{n\to +\mathrm{\infty }}{A}_n$$$$3)studytheserie\mathrm{\Sigma }{A}_n$$ Commented by…