Suppose $k_{n} \rightarrow k$ and $k$ is a constant. I want to show that $kk_{n} > \frac{k^2}{2}$ for a large enough $n$. Could someone give me feedback on my proof?
$\lim_{n\to\infty} kk_{n} = k \lim_{n\to\infty} k_{n} = k^2$, which is clearly bigger than $\frac{k^2}{2}$.