If ∑ a_n , ∑ c_n , and ∑ d_n are all positive series, where ∑ c_n converges and ∑ d_n diverges, then:

1. If a_n ≤ c_n for all n ≥ N for some fixed N, then ∑ a_n converges.

2. If a_n ≥ d_n for all n ≥ N for some fixed N, then ∑ a_n diverges.