Square Numbers = {n^2: n is a natural number} = {1, 4, 9, 16, 25, 36, 49, 64, 81, ...}
The fractions in (a) are 4/9, 9/16, 16/25, 25/36, 36/49, 49/64, 64/81
Triangular numbers = {1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...}
The fractions in (b) are 3/6, 6/10, 10/15, 15/21, 21/28, 28/36, 36/45
The fractions using square numbers are all in their simplest form
T(n+1) = T(n) + 2n + 1 = n(n + 2) + 1
The fractions using triangular numbers are not in their simplest form
T(n+1) = T(n) + n
I am not sure how to express the inductive reasoning.