Edit post : Give 2017 positive integer numbers a1 , a2 , a3 , a4 , ............... a2017 so that 

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Suppose a₁ , a₂ , a₃ , a₄ , ...... , a₂₀₁₇ are different .

And 0 < a₁ < a₂ < .............. < a₂₀₁₇

Since is a positive integer so that we have :

\(\dfrac{1}{a_1}+\dfrac{1}{a_2}+........+\dfrac{1}{a_{2017}}\le\dfrac{1}{1}+\dfrac{1}{2}+.........+\dfrac{1}{2017}< \dfrac{1}{1}+\dfrac{1}{2}+\dfrac{1}{2}...............+\dfrac{1}{2}=1+\dfrac{2016}{2}=1+1008=1009\)

From this , if those numbers are different so that the sum always smaller than 1009 , but those are equal to 1009 , that means there are 2 in 2017 numbers are equal.