Critical Thinking problem please help!?

Question

Make a conjecture about the relationship between there consecutive whole numbers based on this relationship illustrated by numbers, 3,4, and 5:(3X5) =4^2 -1. Can you find a counter example?

Answer 1

for the numbers 1,2,3
1x3=2^2 -1

for the numbers 2,3,4
2x4=3^2 -1

for the numbers 5,6,7
5x7=6^2 -1

for the numbers 6,7,8
6x8=7^2-1

for the numbers 7,8,9
7x9=8^2 -1


for the numbers 11,12,13
11 x 13 =12^2 -1

for some numbers n,n+1,n+2
n x (n+2)= (n+1)^2 - 1

Answer 2

I would conjecture that of three numbers, n-1, n and n+1, that perhaps (n-1)x(n+1) = n^2 - 1. Try it with a few different n. Does it work? Can you find the counter-example, or maybe prove there isn't one? You can do it!