Let \(0<a_1<a_2<a_3<\dots<a_n\) integers. Is it definitely true, that
\[\dfrac{1}{a_1}+\dfrac{1}{\text{lcm}(a_1, a_2)}+\dfrac{1}{\text{lcm}(a_1, a_2, a_3)}+\dots+\dfrac{1}{\text{lcm}(a_1, a_2, a_3, \dots, a_n)}<2?\]

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