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Calculus Level 4

Let SkS_{k} be the area bounded by the curve y=x2(1x)ky=x^2 (1-x)^k and the lines x=0x=0, y=0y=0 and x=1x=1. If limnk=1nSk \displaystyle \lim_{n\to\infty} \sum_{k=1}^n S_k is equal to pq \dfrac pq, where p p and qq are coprime positive integers, find p+qp+q.

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