1. To prove by induction that n! > 2n for n > 3, n  N
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(c) Project Maths Development Team 2011

2. (c) Project Maths Development Team 2011
To prove by induction that n! > 2n for n > 3, n  N
Prove : n! > 2n for n = 4
n! = 4! = 24
24 = 16
24 > 16
True for n = 4
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(c) Project Maths Development Team 2011

3. (c) Project Maths Development Team 2011
To prove by induction that n! > 2n for n > 3, n  N
Assume true for n = k
Therefore k! > 2k
Prove true for n=k+1
Multiply each side by k + 1 (As k>3 hence (k+1) must be positive)
(k + 1)k! > (k + 1)2k
(k + 1)! >(k + 1)2k (Because (k+1)k!=(k+1)!)
(k + 1)! > 2k (k + 1 > 2 since k > 3)
If true for n = k this implies it is true for n = k+1. It is true for n = 4.
Hence k! > 2k for n > 3, n  N
(c) Project Maths Development Team 2011