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.

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