# Maximize this!

Algebra Level 5

Let $${ A }_{ 1 },{ A }_{ 2 }, { A }_{ 3 },...,{ A }_{ k }$$ be a sequence of positive real numbers. Given that $\displaystyle \sum _{ i=1 }^{ k }{ { A }_{ i } } = 1000$

and that $$\prod _{ i=1 }^{ k }{ { A }_{ i } }$$ is maximized, determine $$k$$.

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