If \(\displaystyle \sum_{n=1}^\infty a_n \) diverges and \(0\leq a_n\leq b_n\) for all \(n\), which of the following statements must be true?

We can use the direct comparison test. Since \(a_n\) is always less than \(b_n\), \(\displaystyle \sum_{n=1}^\infty b_n\) must also diverge if \(\displaystyle \sum_{n=1}^\infty a_n\) diverges.