Y by Adventure10
Let
be positive integers such that no one of them is an initial fragment of any other (for example,
is an initial fragment of
and
). Prove that
![\[\frac{1}{x_1}+\frac{1}{x_2}+\ldots+\frac{1}{x_n}<3. \]](//latex.artofproblemsolving.com/f/2/8/f28f787c8b34d5a586c64df314ee34836e9943d3.png)




![\[\frac{1}{x_1}+\frac{1}{x_2}+\ldots+\frac{1}{x_n}<3. \]](http://latex.artofproblemsolving.com/f/2/8/f28f787c8b34d5a586c64df314ee34836e9943d3.png)
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