Extend and generalize:
We use the fact that the sum of the first n odd numbers is n2.
E.g., 1 + 3 + 5 + 7 = 16 = 42.
We also use the fact that, say, 7 + 9 + 11 can be thought of as a difference of squares.
1 + 3 + 5 + 7 + 9 + 11 – (1 + 3 + 5), i.e., 62 – 32.
Thus the denominator in each of these fractions is the sum of the first 2n odd numbers minus the sum of the first n odd numbers:
We are heading toward the formula
