# 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 $\dfrac{1}{a_1}+\ldots+\dfrac{1}{a_n}$.