# Prove inequalities

• Feb 13th 2013, 09:23 AM
raggie29
Prove inequalities
Prove that 4^n > 7n^2 for n > 3
• Feb 13th 2013, 09:37 AM
Plato
Re: Prove inequalities
Quote:

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
$4^{k+1}\ge 7(k+1)^2~?$
• Feb 13th 2013, 09:43 AM
raggie29
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?
• Feb 13th 2013, 10:06 AM
HallsofIvy
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.