Showing that if n is a natural number larger than 3, then n ! >...

Kirsten Bishop

Kirsten Bishop

Answered

2022-11-29

Showing that if n is a natural number larger than 3, then n ! > 2 n
Showing that if n is a natural number larger than 3, then n ! > 2 n
My try:
Base Case:
If n = 4, then 4 ! > 2 4
24 > 16
So, the base case is true.
Assuming P ( k ) is true.
k ! > 2 k
Now we need to show that P ( k + 1 ) is true.
( k + 1 ) ! = 2 k + 1
Proof:
( k + 1 ) ! > ( k + 1 ) k !
( k + 1 ) 2 k
After this I have no idea how to solve further.
Can anyone explain how to continue.

Answer & Explanation

Gwendolyn Case

Gwendolyn Case

Expert

2022-11-30Added 7 answers

After finding out that the base case is true and assuming P ( k ) is true, for P ( k + 1 ) we have
by inductive argument and since k + 1 > 2 we have ( k + 1 ) ! > 2 k + 1

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?