# 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.
×