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My question is the following: Assume a sequence $b_{n}$ which converge. Does a limit for $\frac{1}{b_{n}}$ exist?

My idea ist to use the "Quotient Law for Convergent Sequences" by setting: $a_{n}=1$ and just apply the law. But this sounds a little bit to cheap..

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  • $\begingroup$ You need that $b_n$ does not converge to $0$. $\endgroup$
    – podiki
    Dec 3, 2021 at 22:45

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It doesn't follow. Take $b_n = \frac{1}{n}$.

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  • $\begingroup$ $\frac{1}{b_{n}}= \frac{1}{\frac{1}{n}}$? $\endgroup$
    – Sueton
    Dec 3, 2021 at 22:38
  • $\begingroup$ Yep. $\frac{1}{b_n} = \frac{1}{\frac{1}{n}} = n$, so $\lim \frac{1}{b_n} = \lim n = \infty$. $\endgroup$
    – Adam Neeley
    Dec 3, 2021 at 23:45

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