Category: Limits

Question Number 28617 by abdo imad last updated on 27/Jan/18 $$letgiveasequenceofreals{\left(a_n\right)}_n/a_n>0and$$$$U_n=\frac{a_n}{(1+a_1)(1+a_2)\dots .(1+a_n)}$$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\Sigma\:{u}_{{n}} \:{converges} \…

Question Number 159668 by Ar Brandon last updated on 19/Nov/21 $$\mathrm{Study}\mathrm{the}\mathrm{nature}\mathrm{of}$$$$\mathrm{\Sigma }\frac{n^n}{{\left(\ln n\right)}^{n^2}}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 159646 by cortano last updated on 19/Nov/21 $$\underset{x\to 0}{\lim }\frac{1-{\left(\cos x\right)}^{\sin x}}{x^3}=?$$ Answered by FongXD last updated on 19/Nov/21 $$\mathrm{L}=\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\left(\mathrm{cosx}\right)^{\mathrm{sinx}} }{\mathrm{x}^{\mathrm{3}}…

Question Number 159613 by cortano last updated on 19/Nov/21 Commented by tounghoungko last updated on 19/Nov/21 $$A=\underset{x\to 0}{\lim }\frac{2\sin x(1-\cos x)}{\sin x(1-\cos {}^{3}x)}$$$$A=\underset{x\to 0}{\lim }\frac{2(1-\cos x)}{(1-\cos x)(\cos {}^{2}x+\cos x+1)}$$$$\:{A}=\:\frac{\mathrm{2}}{\mathrm{3}}…

Question Number 159598 by Ar Brandon last updated on 19/Nov/21 $$\mathrm{Determine}\mathrm{the}\mathrm{limits}\mathrm{of}\mathrm{the}\mathrm{following}\mathrm{sums};$$$$u_n=\underset{k=1}{\sum ^n}\frac{n}{{nk}^2+k+1}$$$${v}_{{n}} =\underset{\mathrm{1}\leqslant{k}\leqslant\mathrm{2}{n}} {\sum}\frac{{n}^{\mathrm{2}} }{{kn}^{\mathrm{2}} +{k}^{\mathrm{2}} } \…