Another Pattern

Algebra Level 4

\[\frac{1}{1 \times 2 \times 3} + \frac{1}{2 \times 3 \times 4} + \frac{1}{3 \times 4 \times 5} + ... +\frac{1}{98 \times 99 \times 100} \].

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


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