Category: Limits

Question Number 29836 by abdo imad last updated on 12/Feb/18 $$letgive{u}_n=\sum _{q=1}^n\frac{1}{n^2+q}find{lim}_{n\to +\mathrm{\infty }}(1-{nu}_n)n.$$ Terms of Service Privacy Policy Contact:…

Question Number 160885 by qaz last updated on 08/Dec/21 $$\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }\underset{\mathrm{k}=1}{\sum ^{\mathrm{n}}}\frac{\mathrm{n}+\frac{1}{\mathrm{k}}}{\sqrt{{\mathrm{n}}^2+{\mathrm{k}}^2}}\cdot \sin \frac{1}{\mathrm{n}}=?$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 160875 by cortano last updated on 08/Dec/21 $$\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }\sqrt[\mathrm{n}]{5^{\mathrm{n}}+7^{\mathrm{n}}}=?$$ Answered by MJS_new last updated on 08/Dec/21 $$\left(\mathrm{5}^{{n}} +\mathrm{7}^{{n}} \right)^{\mathrm{1}/{n}}…

Question Number 160825 by qaz last updated on 07/Dec/21 $$\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }{\left[{\int }_0^1{(1+\sin \frac{\pi \mathrm{t}}{2})}^{\mathrm{n}}\mathrm{dt}\right]}^{\frac{1}{\mathrm{n}}}=?$$ Answered by mnjuly1970 last updated on 07/Dec/21 $${answer}\::\:\:\Omega\::=\:{sup}_{\:\left[\:\mathrm{0}\:,\mathrm{1}\:\right]}…

Question Number 160793 by cortano last updated on 06/Dec/21 $$\underset{x\to 0}{\lim }\frac{2^{\cos \mathrm{x}}-2}{{\mathrm{x}}^2}=?$$ Answered by qaz last updated on 06/Dec/21 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{2}^{\mathrm{cos}\:\mathrm{x}} −\mathrm{2}}{\mathrm{x}^{\mathrm{2}}…