1. ## Power Project

Some help with this question would be greatly appreciated!

Determine for which natural numbers k^2 < 2^k and prove your answer.

Power is defined in the following way. Let b be a fixed integer. We define b^k for all integers k >= 0 by:

b^0 := 1

Assuming b^n defined, let b^(n+1) := b^n * b

Thanks!

2. Originally Posted by jstarks44444
Some help with this question would be greatly appreciated!
Determine for which natural numbers k^2 < 2^k and prove your answer.
Is it true for $k=1,~2,~3\text{ or }4~?$
By induction show that if $n\ge5$ then $n^2<2^n$.