(adsbygoogle = window.adsbygoogle || []).push({}); 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 a^{b}> 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)a^{i}

3. The attempt at a solution

So I tried using the binomial theorem to get the value a^{N}.

I get that a^{N}must be greater than (i=0 to n-1)Ʃ(n choose i)a^{i}

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)a^{i}?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Proof Related to the Binomial Theorem

**Physics Forums | Science Articles, Homework Help, Discussion**