Question

Medal + fan
n! > 2^n
Prove that n > 3

Answer 1

Well, what happens if you represent them at n=3?

3*2*1 > 2*2*2

obviously false, however next term added:

4*3*2*1>2*2*2*2

Since 4 is just 2*2, we can divide out 3 of the 2's on both sides to get:

3*1>2

We know 3 is greater than 2, not a problem.

So now from here what happens for higher powers of n? We will be multiplying the left hand side of the inequality by increasingly larger values while the right hand side we will only be multiplying by 2.

That's how I would prove it.

Answer 2

Not allowed.

Answer 3

are you learning induction?

assume true for k, prove for k + 1

Answer 4

hmm ?

Answer 5

What did you mean by prove for K + 1

Answer 6

now go back and find a k where it is true, and it will always be true for all k + 1 's.