A complicated series

Algebra Level 5

Let S=31×2×3+52×3×4+73×4×5+........+3718×19×20 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 S can be represented as abc a \frac{b}{c} , where b,cb,c are coprime. Find a+b+c a + b + c .

Note : This problem is not an original problem.

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