You must prove using the method specified. You must write clearly and in complete sentences. Make sure you read the hidden quantifiers in the sentences so that you can interpret the structure of the sentences correctly.

(3) (6 pts) The domain is integers. Consider the following proposition. For every n 2, 2n 2 + 2n < n3 + 3n.

I have given the start of a proof by contradiction. Fill the blank, complete the proof, and provide a complete proof as your answer. Proof by contradiction. Suppose the statement is false. Then, there exists a specific positive integer n such that n 2, but 2n 2 + 2n n 3 + 3n.