Show that for any natural number n, there is a regular language that is not recognized by any DFA with at most n final states Just as the question asks, I am trying to understand the relationship between the number of accept states a DFA has (not necessarily the total number of states) and the languages it can accept. 

I understand that the pumping lemma can be used to show that if a language has a length greater than the number of states, which is the pumping length, then it may not be a regular language. However, I don't understand how a language can be rejected by a DFA based on the number of accept states it has. 

For example, I know that a* \cup b* is not a regular language because of the pumping lemma, but how do I know that it is not accepted by a DFA with only 1 accept state?
$\{\lambda, a, a^2, \dots, a^n\}$. All states in which these words are accepted must be different, in order to avoid loops (and stay finite).