Category: Relation and Functions

Question Number 32369 by prof Abdo imad last updated on 23/Mar/18 $$provethat{n}^{-\alpha }\sim {\int }_n^{n+1}{t}^{-\alpha }dt$$$$2)provethat\sum _{k=1}^n\frac{1}{k^{\alpha }}\sim \frac{n^{1-\alpha }}{1-\alpha }if\alpha <1and$$$$\sum_{{k}=\mathrm{1}} ^{{n}}…

Question Number 32348 by abdo imad last updated on 23/Mar/18 $$1)letn\in Nand{A}_n={\int }_0^{\pi }\frac{dx}{1+{cos}^2\left(nx\right)}.calculate{A}_n$$$$2)f\in C^0([0,\pi ],R)find{lim}_{n\to \mathrm{\infty }}{\int }_0^{\pi }\frac{f\left(x\right)}{1+{cos}^2\left(nx\right)}dx.$$ Terms…

Question Number 32335 by abdo imad last updated on 23/Mar/18 $$lett⩾0andf\left(t\right)=\frac{t}{\sqrt{1+t}}.provethatthesequence$$$$S_n=\sum _{k=1}^{n}f\left(\frac{k}{n^2}\right)convergesandfinditslimit.$$ Terms of Service Privacy Policy Contact:…

Question Number 32300 by abdo imad last updated on 22/Mar/18 $$calculate\sum _{n=0}^{\mathrm{\infty }}{n}^2{e}^{in\theta }$$$$2)find\sum _{n=0}^{\mathrm{\infty }}{n}^{2}cos\left(n\theta \right)and\sum _{n=0}^{\mathrm{\infty }}{n}^{2}sin\left(n\theta \right)=.$$ Terms…

Question Number 32295 by abdo imad last updated on 22/Mar/18 $$calculate\sum _{k=0}^n(2k+1){(-1)}^k.$$ Commented by prof Abdo imad last updated on 04/Apr/18…