Suppose that $a_n \rightarrow \infty$ and $b_n \rightarrow L$ as $n \rightarrow \infty$, where $L$ is real. Prove from the limit definitions that
(a) $b_n/a_n \rightarrow 0$ as $n \rightarrow \infty$
(b) $a_n+b_n \rightarrow \infty$ as $n \rightarrow \infty$
Sorry guys. This is fairly easy. Just can't figure it out.
I know how to rigorously define each of the separate components, but I am unsure of how to put it together.