MathDB

12

Part of 2000 Baltic Way

Problems(1)

Interesting 'fragment' inequality

Source: Baltic Way 2000

12/17/2010
Let x1,x2,…xnx_1,x_2,\ldots x_n be positive integers such that no one of them is an initial fragment of any other (for example, 1212 is an initial fragment of 12‾,12‾5\underline{12},\underline{12}5 and 12‾405\underline{12}405). Prove that 1x1+1x2+…+1xn<3.\frac{1}{x_1}+\frac{1}{x_2}+\ldots+\frac{1}{x_n}<3.
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