Question

If P(n) is statement "n(n+1)(n+2) is divisible by 12 ".Show that the statement P(3) and P(4)are true but not p(5).

Answer 1

p (3)=3 (3+1)(3+2)
=3×4×5
=60

p (4)=4(4+1)(4+2)
=4×5×6
=120
p (5)=5 (5+1)(5+2)
=5×6×7
=210
so,60 and 120 is divisible by 12 and 210 is not