Find the value of the sum below

Algebra Level 3

\[ \dfrac11 + \dfrac1{1 + 2} + \dfrac1{1 + 2 + 3} + \dfrac1{1 + 2 + 3 + 4} + \cdots+ \dfrac1{1 + 2 + 3 + \cdots+ 2017} \]

If the sum above simplifies to \( \dfrac ab\), where \(a\) and \(b\) are coprime positive integers, then find \( a + b\).

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