Category: Limits

Question Number 4132 by prakash jain last updated on 29/Dec/15 $$\mathrm{Is}\mathrm{there}f\left(n\right)\mathrm{such}\mathrm{that}$$$$\underset{x\to 0}{\lim }\left[\underset{n=1}{\sum ^{\mathrm{\infty }}}f\left(n\right)x^n\right]\ne 0$$$$f\left(n\right)\mathrm{is}\mathrm{independent}\mathrm{of}x.$$ Commented by Yozzii last…

Question Number 69607 by malwaan last updated on 25/Sep/19 $$\mathit{w}\mathit{i}\mathit{t}\mathit{h}\mathit{o}\mathit{u}\mathit{t}\mathit{u}\mathit{s}\mathit{i}\mathit{n}\mathit{g}\mathit{l}\mathit{h}\mathit{o}\mathit{s}\mathit{p}\mathit{i}\mathit{t}\mathit{a}\mathit{l}\mathit{p}\mathit{l}\mathit{e}\mathit{a}\mathit{s}\mathit{e}$$$$\mathit{p}\mathit{r}\mathit{o}\mathit{v}\mathit{e}\mathit{t}\mathit{h}\mathit{a}\mathit{t}$$$$\underset{\mathit{x}\to 0}{\mathit{l}\mathit{i}\mathit{m}}\frac{\mathit{x}-\mathit{s}\mathit{i}\mathit{n}\mathit{x}}{{\mathit{x}}^3}=\frac{1}{6}$$$$\mathit{I}\mathit{w}\mathit{a}\mathit{n}\mathit{t}\mathit{e}\mathit{v}\mathit{e}\mathit{r}\mathit{y}\mathit{m}\mathit{e}\mathit{t}\mathit{h}\mathit{o}\mathit{d}$$$$\mathit{p}\mathit{o}\mathit{s}\mathit{s}\mathit{i}\mathit{b}\mathit{l}\mathit{e}\mathit{b}\mathit{e}\mathit{c}\mathit{a}\mathit{u}\mathit{s}\mathit{e}\mathit{s}\mathit{o}\mathit{m}\mathit{e}\mathit{o}\mathit{n}\mathit{e}$$$$\mathit{c}\mathit{h}\mathit{a}\mathit{l}\mathit{l}\mathit{e}\mathit{n}\mathit{g}\mathit{e}\mathit{m}\mathit{e}$$ Commented…

Question Number 135034 by mnjuly1970 last updated on 09/Mar/21 $$\dots nicecalculus$$$$ifn⩾2and{P}_n=\underset{n=1}{\prod ^{n-1}}sin\left(\frac{k\pi }{n}\right)$$$$find::{lim}_{n\to \mathrm{\infty }}\frac{{nP}_n}{2}{\int }_{\frac{\pi }{6}}^{\frac{\pi }{3}}\frac{cos\left(3x\right)}{{sin}^n\left(x\right)}dx$$ Terms…

Question Number 69478 by Henri Boucatchou last updated on 24/Sep/19 $$\underset{\mathit{n}\to \mathrm{\infty }}{\mathit{l}\mathit{i}\mathit{m}\mathit{s}\mathit{i}\mathit{n}}\left(\mathit{n}\mathit{\pi }\right)=?$$ Commented by mathmax by abdo last updated on 24/Sep/19 $${sin}\left({n}\pi\right)=\mathrm{0}\:\Rightarrow{lim}_{{n}\rightarrow+\infty} {sin}\left({n}\pi\right)=\mathrm{0}…

Question Number 69338 by Rasheed.Sindhi last updated on 22/Sep/19 Commented by Prithwish sen last updated on 22/Sep/19 $$\mathrm{it}\mathrm{is}\mathrm{the}\mathrm{series}\mathrm{of}$$$$1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\dots \dots$$$$\mathrm{tan}^{−\mathrm{1}} \mathrm{x}=\mathrm{x}−\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{3}}+\frac{\mathrm{x}^{\mathrm{5}} }{\mathrm{5}}−\frac{\mathrm{x}^{\mathrm{7}}…