How is this evaluated. Is it k(k+1) or is it (k+1)(k+2). This is the problem if anyone wants to try it out.
Prove by induction on n that n!>2^n for all integers n such that n >or= 4
Proposition: for .
Proof: We will prove the proposition by induction on a variable .
If , we have or , which is true.
Taking , we have
Multiplying by k+1, we have
And since , the minimum value we can have for is 5, so we have
By transitivity, we have
Hence, for , QED