\[\large \displaystyle \int_{0}^\infty\lfloor x+1\rfloor\dfrac{(-1)^{\lfloor x\rfloor}\cdot 2016\cdot { \{x\} }\cdot dx}{2^{\lceil x\rceil}} = \, ? \]

**Notations**:

\( \lfloor \cdot \rfloor \) denotes the floor function.

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

\( \lceil \cdot \rceil \) denotes the ceiling function.

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