If P(n) :

Solution:

P(n) : n! > 2n – 1; n ∈ 

for n = 1,

P(1) : 1! > 21–1

i.e 1 > 2° = 1

i.e 1 > 1

which is false a statement

for n = 2

P(2) : 2! > 22–1

i.e 2 > 21

i.e 2 > 2

which is again a false statement.

for n = 3

P(3) : 3! > 23–1

i.e 6 > 22 = 4

i.e 6 > 4 which is true

for n = 4

P(4) : 4! > 24–1

i.e 24 > 23 = 8 which is true

Hence, P(n) : n! > 2n – 1 is true

for n > 2