If denotes the integral part of real

MATHEMATICS · Subjective · AoPS · Mathematics · Special Functions · Special Functions

Problem

If [x][x] denotes the integral part of real xx, find the value of [14]+[14+1200]+[14+2200]+[14+3200]+⋯+[14+199200].\left[\frac14\right]+\left[\frac14+\frac1{200}\right]+\left[\frac14+\frac2{200}\right]+\left[\frac14+\frac3{200}\right]+\cdots+\left[\frac14+\frac{199}{200}\right].

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