First, we have
We know from the previous exercise (Section 7.4, Exercise #6) that
We also know (from the example on page 277) that
Therefore, using Theorem 7.2 (a), the linearity property of we have
However, if is even and if is odd. Therefore we can sum over just the odd values of . Let and we have
Where we have renamed the index of summation in the final step so that the sum is over as in the book.