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 - Maths - Principle of Mathematical Induction

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)

Ashwini Kumar · Accepted Answer

pn:nn+1n+2 is divisible by 12
For n=3nn+1n+2=3×4×5=60As, 60 is exactly divisible by 12, therefore statement is true for n=3
For n=4nn+1n+2=4×5×6=120As, 120 is exactly divisible by 12, therefore statement is true for n=4
For n=5nn+1n+2=5×6×7=210As, 210 is not exactly divisible by 12, therefore statement is not true for n=5

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).