If P(n) :

Solution:

P(n) : n2 < 2n, n ∈ N

for n = 1,

P(1) : 1 < 2  which is true statement

for n = 2,

P(2) : 22 < 22   which is not true/false statement

for n = 3,

P(3) : (3)2 < 23

i.e 9 < 8 which is a false statement

for n = 4,

P(4) : (4)2 < 24

i.e 16 < 4 × 4 = 16

which is a false statement

for n = 5,

P(5) : (5)2 < 25

i.e 25 < 32

which is a true statement

for n = 6,

P(6) : (36) < 26

i.e 36 < 4 × 4 × 4 = 64

Which is a true statement

for $n=7, P(7): 49<2^{7}=128$ which is again true statement

Hence, P(n) : n2 < 2n is true for n ≥ 5