Newton + Telescope

Algebra Level 4

If \(x^2+x-1=0\) then evaluate \[\large \sum_{r=0}^{2016} \Big (\frac {2017-r}{2}\Big )^{\lceil \{\frac {r}{2}\} \rceil}\cdot x^r\].

Notation: \( \{ \cdot \} \) denotes the fractional part function.

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