So if you pick some triangle number A = 1/2n(n+1), a consecutive triangle number would be B= 1/2(n+1)(n+2). Note that B is smaller than A as it has a larger denominator so when it comes to triangle numbers in order, it goes B, then A.

If we put these numbers in ascending order into a ratio, we get:

1/2(n+1)(n+2):1/2n(n+1)

Now if we multiply both sides by 2n(n+1), we can get rid of the denominat... more