1. The problem statement, all variables and given/known data Use the above to prove that given a rational number a > 1 and A any other rational number, there exists b ε N such that ab > A. 2. Relevant equations The above refers to the proving, by use of both induction and binomial theorem, that (1+a)n ≥ 1+na. Binomial Theorem: (i=0 to n)Ʃ(n choose i)ai 3. The attempt at a solution So I tried using the binomial theorem to get the value aN. I get that aN must be greater than (i=0 to n-1)Ʃ(n choose i)ai So how do I choose an N so that this holds? Could you just let N > (i=0 to n-1)Ʃ(n choose i)ai?