Brute Force No More

Algebra Level 5

π+π+12016+π+22016++π+20152016+1=? \large \left \lceil \lfloor \pi \rfloor + \left \lfloor \pi + \dfrac{1}{2016} \right \rfloor + \left \lfloor \pi + \dfrac{2}{2016} \right \rfloor + \cdots + \left \lfloor \pi + \dfrac{2015}{2016} \right \rfloor \right \rceil + 1 =\, ?

Notations: \lfloor \cdot \rfloor denotes the floor function and \lceil \cdot \rceil denotes the ceiling function.


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