Alternatively, we could observe that every even term is 0, so we only need to generate odd terms. We could have expressed the bn term as:

math expression

To generate odd numbers for our series, we need to use:

math expression

We also need to generate only odd numbers for the sine terms in the series, since the even ones will be 0.

So the required series this time is:

math expression

The first four terms series are once again:

math expression