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Calculus Level 5

Let \(s_1, \ldots, s_n\), with \(n\) being an integer \(\geq 1\), be a series of positive real numbers such that

\[\displaystyle \sum_{i=1}^n s_i = 271.\]

If the maximum value of

\[\displaystyle \prod_{k=1}^n s_k = \dfrac {a^x}{b^y}\]

where \(a\) and \(b\) are square-free coprime positive integers, and \(x\) and \(y\) being positive integers greater than 1, find \(a+x+b+y\).

Note: \( n \) is variable.


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