Sum of Fractions

Algebra Level 4

\( S = \frac {1}{1\times 2 \times 3} + \frac {1}{2\times 3 \times 4} + \ldots + \frac {1} {(n)(n+1)(n+2)} \) \(+ \ldots +\frac {1}{14 \times (14+1) \times (14+2)} = \frac {a} {b}, \) where \(a\) and \(b\) are positive, coprime integers. What is the value of \( a + b \)?

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