`A = 1 + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + \...+ \frac{1}{2011 \times 2012}`

`A = 1 + \frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{4} + \... + \frac{1}{2011} - \frac{1}{2012}`

`A = 1 + \frac{1}{2} - \frac{1}{2012}`

`A = \frac{3}{2} - \frac{1}{2012}`

`A = \frac{3018}{2012} - \frac{1}{2012}`

`A = \frac{3017}{2012}`

`---------------`

`B = \frac{3}{4} + \frac{3}{4 \times 5} + \frac{3}{5 \times 6} + \... + \frac{3}{2011 \times 2012}`

`B = \frac{3}{4} + \frac{3}{4} - \frac{3}{5} + \frac{3}{5} - \frac{3}{6} + \... + \frac{3}{2011} - \frac{3}{2012}`

`B = \frac{3}{4} + \frac{3}{4} - \frac{3}{2012}`

`B = \frac{6}{4} - \frac{3}{2012}`

`B = \frac{3}{2} - \frac{3}{2012}`

`B = \frac{3018}{2012} - \frac{3}{2012}`

`B = \frac{3015}{2012}`