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Calculus Level 5

Let \(S_{k}\) be the area bounded by the curve \(y=x^2 (1-x)^k \) and the lines \(x=0\), \(y=0\) and \(x=1\). If \( \displaystyle \lim_{n\to\infty} \sum_{k=1}^n S_k \) is equal to \( \dfrac pq\), where \( p\) and \(q\) are coprime positive integers, find \(p+q\).

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