\(\frac{1}{1\cdot2\cdot3}\)

Algebra Level 3

\[\large \dfrac{1}{1 \cdot 2 \cdot 3}+\frac{1}{2 \cdot 3 \cdot 4}+\frac{1}{3 \cdot 4\cdot 5}+\cdots \]

If the series above can be expressed as \( \dfrac pq\), where \( p\) and \(q\) are coprime positive integers, find \(p+q\).

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