well it looks like i didn't give the right first problem. The (-1) on the right is supposed to be (-1)^n.
anyways, i've gotten number 1 somewhat done. I set n = 0, and that checked out, then I got n = k, and then did the k+1. What I'm left with now is the following.
... = ((2^(k+1))/(3*2^k)) + (((-1)^k)/(3*2^k)) + (-1/2)^(k+1)
I'm really not sure what to do after this point...