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Closed form expression for sum of floor of square roots To find the sum of ⌊ k−−√ ⌋ from k=0 to k=m, I first realized that the floor of the square root gives n for the interval [n2, (n + 1)2) Within that interval, I found that the number of integers is given by:
How do the floor and ceiling functions work on negative numbers? The correct answer is it depends how you define floor and ceil You could define as shown here the more common way with always rounding downward or upward on the number line OR Floor always rounding towards zero Ceiling always rounding away from zero E g floor (x)=-floor (-x) if x<0, floor (x) otherwise If gravity were reversed, the ceiling would become the floor So from a physics
Floor and ceiling functions - TeX - LaTeX Stack Exchange Is there a convenient way to typeset the floor or ceiling of a number, without needing to separately code the left and right parts? For example, is there some way to do $\\ceil{x}$ instead of $\\lce