Show that

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.