show that the sum of the first 2n terms of the series 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5........................is the same as the sum of the first n terms of the series 1/1*2 + 1/2*3 + 1/3*4 +1/4*5................... Do these series converge? what is the sum of the first 2n+1 terms of the first series and how to get the sum?