2. a) Show by mathematical induction that

1/2 + 2/2^2 + 3/2^3 + ... + n/2^n = 2 - n+2/2^n

My work:

1. Show p(1) true. I did this part.

2. Assume p(k) true => assume p(k+1) true

I'm a bit stuck here. Here's how I set it up

(2 - k+2 / 2^k) + (k+1 / 2^k+1) = (2 - k+2 / 2^k) + (k+1 / 2^k+1)

I think all I have to do is simplify the right side so that it equals 2 - k+3 / 2^k+1. Please help.