If ∑n=1∞an\displaystyle \sum_{n=1}^\infty a_n n=1∑∞an diverges and 0≤an≤bn0\leq a_n\leq b_n0≤an≤bn for all nnn, which of the following statements must be true?
We can use the direct comparison test. Since ana_nan is always less than bnb_nbn, ∑n=1∞bn\displaystyle \sum_{n=1}^\infty b_nn=1∑∞bn must also diverge if ∑n=1∞an\displaystyle \sum_{n=1}^\infty a_nn=1∑∞an diverges.