Let's telescope

Algebra Level 4

\[\large{ \dfrac{1}{1^4 + 1^2 + 1} + \dfrac{2}{2^4 + 2^2 + 1} + \ldots + \dfrac{2016}{2016^4 + 2016^2 + 1} ~=~?}\]

Give your answer to 3 decimal places.

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