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..


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