You want the difference between your sum (through some N) and the number the series converges to to be less than epsilon.
Let N=3, then your sum is 1 + (1/2) + (1/4) + (1/8) = 1.875
|1.875-2| = .125 = (1/8) (Noting that the series converges to 2)
So at N=3, the difference = epsilon. Therefore, for n > N, the difference will be less than epsilon=(1/8).
Now just pick some more epsilons and see how many terms it takes to get a difference less than it (your chosen epsilon that is!)
Hope that helps.