Another Pattern

Algebra Level 4

11×2×3+12×3×4+13×4×5+...+198×99×100\frac{1}{1 \times 2 \times 3} + \frac{1}{2 \times 3 \times 4} + \frac{1}{3 \times 4 \times 5} + ... +\frac{1}{98 \times 99 \times 100} .

The expression above can be expressed in a form of 1p1q \dfrac{1}{p} - \dfrac{1}{q}, where pp and qq are positive integers. Find the value of p+qp+q.


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