What is the general function expansion of summation[(1/2^k)(ln(x-y+2^(k-… k=1, n=infinity.?

I know this function converges, but I am looking for a general function expansion of summation[(1/2^k)(ln(x-y+2^(k-1))], k=1, n=infinity. That is to say, I want to express the summation as f(n,x,y)=something.