Question

How do I start this proof:
P(k) -> P(k+1) where P(b) = b(b+1)(b+2)/3

Answer 1

In other words prove that if k(k+1)(k+2)/3 is true then (k+1)(k+2)(k+3)/3 must be true

Answer 2

Is your question `if 3 divides k(k+1)(k+2), then 3 divides (k+1)(k+2)(k+3)` ?