A complicated series

Algebra Level 4

Let $S = \frac{3}{1\times 2 \times 3} + \frac{5}{2 \times 3 \times 4} + \frac{7}{3 \times 4 \times 5} +........+ \frac{37}{18 \times 19 \times 20}$ $S$ can be represented as $a \frac{b}{c}$ , where $b,c$ are coprime. Find $a + b + c$ .

Note : This problem is not an original problem.