Category: Limits

Question Number 210769 by zhou0429 last updated on 19/Aug/24 Commented by Frix last updated on 19/Aug/24 $$\int \frac{dx}{x^n+1}=x{\times }_2{F}_1(1,\frac{1}{n};\frac{n+1}{n};-x^n)+C$$ Terms of…

Question Number 210549 by universe last updated on 12/Aug/24 $$\mathrm{let}\mathrm{a}\mathrm{sequence}\mathrm{be}\mathrm{difined}\mathrm{as}$$$${\mathrm{a}}_{\mathrm{n}}={\mathrm{a}}_{\mathrm{n}-1}+\frac{2\cos \left(\frac{{\mathrm{a}}_{\mathrm{n}-1}}{2}\right)}{2\sin \left(\frac{{\mathrm{a}}_{\mathrm{n}-1}}{2}\right)-1},{\mathrm{a}}_0=0$$$$\mathrm{find}\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }{\mathrm{a}}_{\mathrm{n}}=?$$ Answered by…

Question Number 209926 by depressiveshrek last updated on 26/Jul/24 $$\underset{n\to \mathrm{\infty }}{\lim }\frac{1}{3n+1}+\frac{1}{3n+2}+\dots +\frac{1}{4n}$$ Commented by Frix last updated on 26/Jul/24 $$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{1}}{\mathrm{3}{n}+{k}}\:={H}_{\mathrm{4}{n}} −{H}_{\mathrm{3}{n}} \…

Question Number 209434 by justenspi last updated on 10/Jul/24 $$Help$$ Commented by justenspi last updated on 10/Jul/24 Commented by Berbere last updated on…

Question Number 209220 by alcohol last updated on 04/Jul/24 Answered by Berbere last updated on 04/Jul/24 $$SAB,SAC\mathrm{\&}ABCcestclaire\left(AS\right)\mathrm{\perp }\left(ABC\right)\mathrm{\&}ABCrectangle$$$$\Rightarrow{SA}^{\mathrm{2}} +{AB}^{\mathrm{2}} ={SB}^{\mathrm{2}} ;{SA}^{\mathrm{2}} +{AC}^{\mathrm{2}} ={SC}^{\mathrm{2}} ;{CA}^{\mathrm{2}}…