# Math Help - Prove inequalities

1. ## Prove inequalities

Prove that 4^n > 7n^2 for n > 3

2. ## Re: Prove inequalities

Originally Posted by raggie29
Prove that 4^n > 7n^2 for n > 3
Is it true for $n= 3~?$

If $k>3$ and it is true that $4^k\ge 7k^2$ does it follow that
$4^{k+1}\ge 7(k+1)^2~?$

3. ## Re: Prove inequalities

Yes it is true for n=3 since, 4^n =64 and 7n^2 = 63

So yes it does followe the k+1 example is this correct?

4. ## Re: Prove inequalities

Yes, that is "proof by induction". If a statement, depending on n, is true when n= 3, and, whenever it is true for n= k, it is also true that n= k+1.