Category: Limits

Question Number 30491 by abdo imad last updated on 22/Feb/18 $$let{A}_n=\sum _{k=1}^n\frac{n}{n^2+k^2}find{lim}_{n\to \mathrm{\infty }}{A}_n.$$ Terms of Service Privacy Policy…

Question Number 161553 by qaz last updated on 19/Dec/21 $$\underset{\mathrm{t}\to +\mathrm{\infty }}{\lim t}\underset{\mathrm{k}=0}{\sum ^{\mathrm{\infty }}}\frac{{(-1)}^{\mathrm{k}}}{\sqrt{{\mathrm{k}}^2+{\mathrm{t}}^2}}=?$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 30482 by abdo imad last updated on 22/Feb/18 $$findS=\sum _{p⩾1,q⩾1and\hat{D}(p,q)=1}\frac{1}{p^2{q}^2}.$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 161533 by mathlove last updated on 19/Dec/21 Commented by cortano last updated on 19/Dec/21 $$\underset{x\to 0}{\lim }\frac{{\left(\sqrt{1+x^2+x}\right)}^{2020}-{\left(\sqrt{1+x^2-x}\right)}^{2020}}{x}$$$$\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+\mathrm{1010}\left({x}^{\mathrm{2}}…

Question Number 95980 by john santu last updated on 29/May/20 $$\mathrm{If}\underset{x\to 3}{\lim }\frac{\sqrt{3\mathrm{x}+7}-\sqrt[3]{20\mathrm{x}+4}+a\mathrm{x}+b}{{(x-3)}^2}$$$$\mathrm{exist},\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{value}\mathrm{of}ab$$ Answered by i jagooll last updated on 29/May/20…