# Convergence of 1/$b_{n}$ [closed]

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..

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

It doesn't follow. Take $$b_n = \frac{1}{n}$$.
• $\frac{1}{b_{n}}= \frac{1}{\frac{1}{n}}$? Dec 3, 2021 at 22:38
• Yep. $\frac{1}{b_n} = \frac{1}{\frac{1}{n}} = n$, so $\lim \frac{1}{b_n} = \lim n = \infty$. Dec 3, 2021 at 23:45