Showing that if n is a natural number larger than 3, then n!>2^n

Kirsten Bishop

Kirsten Bishop

Answered question

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

Beginner2022-11-30Added 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

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