Is quite easy: let S be the total sum of the series. If you divide by 2 every term you get 1/2+1/4+1/8 etc, i.e. S - 1. So
S/2 = S - 1 - > S/2 = 1 - > S = 2
S/2 = 1
This can be generalized for every series of 1/n^m. It can be demonstrated that the sum converge if and only if m is > 1. The first series ha m = 1 and does not converge.