Make a conjecture about the relationship between three consecutive

Question

 Make a conjecture about the relationship between three consecutive while numbers based on this relationship illustrated by the numbers 3,4 and 5: (3×5)=4^2-1. Can you find a counterexample.

Answer 1

Three consecutive whole numbers:

n, n+1, and n+2

n(n+2) = (n+1)² = 1

n² + 2n = n² + 2n + 1 - 1

0 = 1 - 1

1 = 1

 

True for all whole numbers