Walk like an Egyptian

Let n>0 be a fixed positive integer and let a_1,\ldots, a_n be distinct positive integers such that

\dfrac{1}{a_1}+\ldots+\dfrac{1}{a_n}<1.

Find the maximum possible value of \dfrac{1}{a_1}+\ldots+\dfrac{1}{a_n}.

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Walk like an Egyptian

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