Let \(a_n=\dfrac{2n+1}{n^3+4}\) and \(b_n=\dfrac1{n^2}\). Compute \(\displaystyle\lim_{n\to\infty}\frac{a_n}{b_n}\). (If the limit is finite and positive, both series behave alike.)
A test that decides whether a series \(\sum a_n\) of nonnegative terms converges by comparing it with another series \(\sum b_n\) such that \(a_n\le b_n\).