Question

Use the method of mathematical induction to show that n! > 2n for all positive integers n is equal to or greater than 4. Thanks in advance :)

Answer 1

1º step check if it is correct for n =4
4!=24>2*4=8 OK
2º step supose it's correct for n=m and prove it's correct for n=m+1
(m+1)!=(m+1)*m!
but we suposed it's correct for n=m, so:
(m+1)*m!>(m+1)*2m
and since m>0
(m+1)*2m>(m+1)2 which proves the statment

Answer 2

@kevinw19

Answer 3

Thank you! It's much appreciated :)

Answer 4

yw