Category: Relation and Functions

Question Number 30486 by abdo imad last updated on 22/Feb/18 $$letgive{a}_n=\prod _{k=1}^{n}cos\left(\frac{\pi }{(k+2)!}\right)and$$$$b_n=\prod _{k=1}^{n}sin\left(\frac{\pi }{(k+2)!}\right)$$$$1)findaequivalentfoe{a}_{n}and{b}_n$$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{equivalent}\:{of}\:{a}_{{n}} .{b}_{{n}}…

Question Number 30484 by abdo imad last updated on 22/Feb/18 $$1)provethatiffisdecreasingfunctionwehave$$$${\int }_n^{n+1}f\left(t\right)dt<f\left(n\right)<{\int }_{n-1}^{n}f\left(t\right)dt.$$$$\left.\mathrm{2}\right)\:{let}\:{put}\:\:{S}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}^{\mathrm{2}} } \:\:\:\frac{\mathrm{1}}{\mathrm{2}\sqrt{{k}}}\:.{calculate}\:\left[{S}_{{n}} \right]. \…

Question Number 30443 by abdo imad last updated on 22/Feb/18 $$let{w}_n\left(x\right)=\sum _{k=1}^n\frac{x^k}{k}find{w}_n\left(x\right)for\mid x\mid <1$$$$2)find{lim}_{n\to \mathrm{\infty }}{w}_n\left(x\right).$$ Terms of Service…

Question Number 30439 by abdo imad last updated on 22/Feb/18 $$letF\left(x\right)=\sum _{n=1}^{\mathrm{\infty }}\frac{{(-1)}^{n-1}}{n^x}calculate\frac{dF}{dx}\left(x\right).$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 30436 by abdo imad last updated on 22/Feb/18 $$let\phi \left(x\right)=1-2^{1-x}provethat$$$$\phi \left(x\right)=(x-1)ln2-\frac{{\left(ln2\right)}^2}{2}{(x-1)}^2+o\left({(x-1)}^2\right).$$ Commented by prof Abdo imad last…