Category: Limits

Question Number 215739 by universe last updated on 16/Jan/25 Answered by MrGaster last updated on 19/Jan/25 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{n}+\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\sum}}{n}^{{k}} }{\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}^{{n}} } \…

Question Number 215667 by mathlove last updated on 14/Jan/25 $$\underset{x\to 1}{\lim }sec\left(\frac{\pi }{2}x\right)(arctanx-\frac{\pi }{4})=?$$ Answered by issac last updated on 14/Jan/25 $$\sec \left(\frac{\pi }{2}\right)(\arctan \left(1\right)-\frac{\pi }{4})$$ Commented by…

Question Number 215051 by MrGaster last updated on 27/Dec/24 $$$$$$\underset{n\to \mathrm{\infty }}{\lim }\underset{k=1}{\prod ^n}\frac{k^2+1}{\sqrt{k^2+4}}=?$$$$$$ Answered by MathematicalUser2357 last…

Question Number 214712 by efronzo1 last updated on 17/Dec/24 $$\cancel{\underset{―}{\underbrace{\mathit{x}}}}$$ Answered by mr W last updated on 17/Dec/24 $$r^2-3r+2=0$$$$\left({r}−\mathrm{1}\right)\left({r}−\mathrm{2}\right)=\mathrm{0} \…

Question Number 214485 by depressiveshrek last updated on 09/Dec/24 $$\underset{n\to \mathrm{\infty }}{\lim }(\frac{1}{2\cdot 4}+\frac{1}{5\cdot 7}+\dots +\frac{1}{(3n-1)(3n+1)})$$ Answered by mr W last updated on 10/Dec/24 $$\psi\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{3}}\right)=−\gamma+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{{n}}−\frac{\mathrm{1}}{{n}−\frac{\mathrm{1}}{\mathrm{3}}}\right) \…