Category: Relation and Functions

Question Number 32998 by abdo imad last updated on 09/Apr/18 $$calculate\sum _{n=1}^{\mathrm{\infty }}\frac{4n+1}{n^2{(3n+1)}^2}.$$ Commented by abdo imad last updated on 15/Apr/18…

Question Number 32997 by abdo imad last updated on 09/Apr/18 $$calculate\sum _{n=0}^{\mathrm{\infty }}\frac{2n+3}{{(n+1)}^2{(n+2)}^2}$$ Commented by abdo imad last updated on 10/Apr/18…

Question Number 32989 by abdo imad last updated on 09/Apr/18 $$letgivef\left(x\right)=\frac{\sqrt{2+x}-\sqrt{2-x}}{x}$$$$find{f}^{-1}\left(x\right)andcalculate{\left(f^{-1}\left(x\right)\right)}^{{}^{\prime }}.$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 32937 by abdo imad last updated on 06/Apr/18 $$letgive\mid x\mid <1provethat$$$$\sum _{n=1}^{\mathrm{\infty }}\frac{sin\left(n\theta \right)}{n}{x}^n=arctan\left(\frac{xsin\theta }{1-xcos\theta }\right).$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 32936 by abdo imad last updated on 06/Apr/18 $$letgive\mid x\mid <1provethat$$$$\sum _{n=1}^{\mathrm{\infty }}\frac{cos\left(n\theta \right)}{n}{x}^n=-\frac{1}{2}ln(1-2xcos\theta +x^2).$$ Terms of Service Privacy Policy Contact:…