Simply Linear

Algebra Level 5

\[ \sum_{n=0}^{2015} (-1)^\left\lfloor\left(\frac{n+1}{2}\right)\right\rfloor \cdot (x + n)^3 = 0 \]

Let \(\alpha \) be the root of the above equation. Find \(2\alpha + 2016\).

Notations

  • Floor function is the exponent of (-1).
  • \( \lfloor \cdot \rfloor \) denotes the floor function.
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