# 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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