a) Sketch:

b) Since the function is even, we have b_n = 0.

In this example, L = π.

We have:

To find a_n, we use a result from before:

We have:

When n is odd, the last line gives us .

When n is even, the last line equals 0.

For the series, we need to generate odd values for n. We need to use (2n - 1) for n = 1, 2, 3,...

So we have:

Check: The graph for the first 40 terms: