Extend and generalize:

We use the fact that the sum of the first *n* odd numbers is *n*^{2}.

E.g., 1 + 3 + 5 + 7 = 16 = 4^{2}.

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., 6^{2} – 3^{2}.

Thus the denominator in each of these fractions is the sum of the first 2*n* odd numbers minus the sum of the first *n* odd numbers:

We are heading toward the formula