# 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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