# 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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