Real analysis sequence convergence problem

Sorry for not using LaTeX, i don't know how to use ithere's my problem

• i should mention that the sequence $\frac{m_n}{k_n}$ is not a constant sequence.

$\text{If } \left\{ \frac{m_n}{k_n} \ne b \right\} \in (\mathbb{Q} > 0) \land \lim_{n \to \infty} \frac{m_n}{k_n} = a \in \mathbb{R} \Rightarrow \lim_{n \to \infty} \frac{1}{k_n} = 0$

Sorry if the latex isn't clear enought, i tried my best.

here's the solution my prof. has given but i don't understand it at all