Category: Relation and Functions

Question Number 161387 by savitar last updated on 17/Dec/21 $$sin\sqrt{1+{\pi }^2{n}^2}\sim \frac{{(-1)}^n}{2\pi n}?$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 95839 by mathmax by abdo last updated on 28/May/20 $$\mathrm{solve}{\mathrm{y}}^{\left(3\right)}-{2\mathrm{y}}^{\left(2\right)}+3\mathrm{y}-2\mathrm{y}=\mathrm{sinx}$$ Commented by john santu last updated on 28/May/20 $$\mathrm{homogenous}\:\mathrm{solution}…

Question Number 95837 by mathmax by abdo last updated on 28/May/20 $$\mathrm{let}\mathrm{p}\left(\mathrm{x}\right)={(1+\mathrm{ix}+{\mathrm{x}}^2)}^{\mathrm{n}}-{(1-\mathrm{ix}+{\mathrm{x}}^2)}^{\mathrm{n}}$$$$1)\mathrm{determine}\mathrm{roots}\mathrm{of}\mathrm{p}\left(\mathrm{x}\right)$$$$2)\mathrm{find}\mathrm{p}\left(\mathrm{x}\right)\mathrm{at}\mathrm{form}\mathrm{\Sigma }{\mathrm{a}}_{\mathrm{i}}{\mathrm{x}}^{\mathrm{i}}$$$$3)\mathrm{ddtermne}\mathrm{p}\left(\mathrm{x}\right)\mathrm{at}\mathrm{form}\arctan$$$$\left.\mathrm{4}\right)\:\mathrm{factorize}\:\mathrm{p}\left(\mathrm{x}\right)\:\mathrm{inside}\:\mathrm{C}\left[\mathrm{x}\right] \…

Question Number 95784 by abdomathmax last updated on 27/May/20 $$\mathrm{calculate}\sum _{\mathrm{n}=1}^{\mathrm{\infty }}\frac{{\mathrm{H}}_{\mathrm{n}}}{{\mathrm{n}}^2}$$$${\mathrm{H}}_{\mathrm{n}}=\sum _{\mathrm{k}=1}^{\mathrm{n}}\frac{1}{\mathrm{k}}$$ Terms of Service Privacy…

Question Number 30217 by abdo imad last updated on 18/Feb/18 $$provethat\mathrm{\forall }n\in N^{★}\frac{1}{\sqrt{n}}-\frac{1}{\sqrt{n+1}}⩾\frac{1}{2(n+1)\sqrt{n+1}}$$$$2)provethat{u}_n=\sum _{k=1}^n\frac{1}{k\sqrt{k}}isconvergente.$$ Terms of Service Privacy Policy Contact:…