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icestone111
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Homework Statement
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.
Homework 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
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?