If denotes the greatest integer function then the extreme values of the function ,

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

If [x][x] denotes the greatest integer function then the extreme values of the function f(x)=[1+sin⁡x]+[1+sin⁡2x]+⋯+[1+sin⁡nx]f(x) = [1 + \sin x] + [1 + \sin 2x] + \dots + [1 + \sin nx] , n∈I+n \in I^+ , x∈(0,π)x \in (0, \pi) are (1) (n−1)(n-1) (2) nn (3) (n+1)(n+1) (4) (n+2)(n+2)

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