I have been trying to calculate the following limit of a fractional part without much success, as I am not very competent at mathematics. Could anyone provide any help please?
$lim_{x \to \infty} \frac{1}{x+1}\sum_{k=0}^x \{k/c\}$
2026-03-28 15:20:26.1774711226
Limit of summation of fractional parts
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If c is irrational (but not zero), k/c has uniform distribution in (0,1). Thus the average goes to 0.5. The rational case can be more difficult.