The problem is asking to prove that the series either converges or diverges. I think I know how to prove divergence but I need someone to confirm. The series is the sum from 1 to infinity of:

(2^(n-1)+1)/2^n

Given that the sum does diverge (right?), you can simplify and say that the original problem, for all values of N > 1, is greater than

Since that equation always yields a value a 1/2, the sum diverges, and since the original sum is greater than that, it must diverge too. Is everything correct?