Thread: 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!

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
By induction show that if then .