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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