Category: Limits

Question Number 68965 by anaplak last updated on 17/Sep/19 Commented by anaplak last updated on 17/Sep/19 $$sirpleasegivemethesolutionshowingbytakingrighthandlimit$$$$imeantosayindetailed$$ Commented by kaivan.ahmadi last…

Question Number 3297 by prakash jain last updated on 09/Dec/15 $$\mathrm{Is}\mathrm{the}\mathrm{following}\mathrm{series}\mathrm{convergent}$$$$\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{1}{{\left(\ln n\right)}^{\ln \left(\ln n\right)}}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 3138 by prakash jain last updated on 05/Dec/15 $$\mathrm{Prove}\mathrm{or}\mathrm{disprove}\mathrm{that}$$$$\mathrm{S}=\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{1}{n^k},k\in {\mathbb{Z}}^{+},k>1\mathrm{is}\mathrm{irrational}.$$ Commented by 123456 last updated on…

Question Number 134171 by liberty last updated on 28/Feb/21 $$\underset{x\to 0}{\lim }\frac{1+\sin \mathrm{x}-\cos \mathrm{x}}{1+\sin \left(\mathrm{px}\right)-\cos \left(\mathrm{px}\right)}=?$$ Answered by malwan last updated on 28/Feb/21 $$\underset{x\to 0}{lim}\frac{1+(x-\dots )-(1-\dots )}{1+(px-\dots )-(1-\dots )}=\frac{1}{p}$$ Answered…

Question Number 68554 by Mikael last updated on 13/Sep/19 Commented by Prithwish sen last updated on 13/Sep/19 $$\mathrm{li}\underset{\mathrm{n}\to \mathrm{\infty }}{\mathrm{m}}\frac{1}{\mathrm{n}}[\frac{1}{1+\frac{0}{\mathrm{n}}}+\frac{1}{1+\frac{1}{\mathrm{n}}}+\dots \dots +\frac{1}{1+\frac{\mathrm{n}-1}{\mathrm{n}}}]$$$$=\frac{\mathrm{1}}{\boldsymbol{\mathrm{n}}}\underset{\boldsymbol{\mathrm{r}}=\mathrm{0}} {\overset{\boldsymbol{\mathrm{n}}−\mathrm{1}} {\sum}}\:\:\boldsymbol{\mathrm{lim}}\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\:}\frac{\mathrm{1}}{\mathrm{1}+\frac{\boldsymbol{\mathrm{r}}}{\boldsymbol{\mathrm{n}}}}\:=\:\underset{\mathrm{0}} {\overset{\mathrm{1}}…