See figure attached for problem statement as well as my attempt.

I'm not entirely sure if I've done the sketch in part a) correctly, can someone verify this for me?

Also, when solving for $\displaystyle a_{n}$ I noticed that all even values of n will give me 0. I tried to rewrite this so that only odd n's are valid.

Can I do this, and am I correct in doing so?

Can anyone else spot any other problems?

Thanks again!