Category: Limits

Question Number 27189 by abdo imad last updated on 02/Jan/18 $$letgive{S}_n=\sum _{p=1}^{p=n}arctan\left(\frac{1}{2p^2}\right)find{lim}_{n->\propto }{S}_n.$$ Answered by prakash jain last updated…

Question Number 158204 by tounghoungko last updated on 01/Nov/21 $$\underset{x\to \mathrm{\infty }}{\lim }(\sin \sqrt{x+1}-\sin \sqrt{x})=?$$ Answered by ajfour last updated on 01/Nov/21 $$L=\underset{x\to \mathrm{\infty }}{\lim 2cos}\left(\frac{\sqrt{x}+\sqrt{x+1}}{2}\right)\sin \left(\frac{\sqrt{x+1}-\sqrt{x}}{2}\right)$$$$=\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}2cos}\:\left(\frac{\frac{\mathrm{1}}{\:\sqrt{{h}}}+\frac{\sqrt{{h}+\mathrm{1}}}{\:\sqrt{{h}}}}{\mathrm{2}}\right)\mathrm{sin}\:\left(\frac{\frac{\sqrt{{h}+\mathrm{1}}−\mathrm{1}}{\:\sqrt{{h}}}}{\mathrm{2}}\right)…

Question Number 158203 by tounghoungko last updated on 01/Nov/21 $$\underset{n\to \mathrm{\infty }}{\lim }\underset{k=1}{\sum ^n}\frac{1}{n}.e^{\frac{2k+1}{k}}=?$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 27098 by abdo imad last updated on 02/Jan/18 $$letgiveS\left(x\right)=\sum _{n=1}^{\propto }\frac{x^n}{n}andW\left(x\right)=\sum _{n=1}^{\propto }\frac{{(-1)}^n{x}^n}{n^2}$$$$calculateS\left(x\right).W\left(x\right).inthatweknow/x/<1.$$ Commented by…

Question Number 92577 by jagoll last updated on 08/May/20 $$\underset{x\to \mathrm{\infty }}{\lim }\frac{\ln \mathrm{x}}{\mathrm{x}}$$ Commented by Tony Lin last updated on 08/May/20 $$\underset{x\to \mathrm{\infty }}{\lim }\frac{lnx}{x}$$$$=\underset{{x}\rightarrow\infty}…