query: Finite sum of floor function.
positive_passages.docid: 41840
positive_passages.text: How do I evaluate this sum(involving the floor function)?
negative_passages.docid: 125981
negative_passages.text: Closed-Form Solution to Infinite Sum
negative_passages.docid: 19064
negative_passages.text: Proof about floor function: $\lfloor x\rfloor+\lfloor x + \frac{1}{n} \rfloor+\cdots + \lfloor x + \frac{(n-1)}{n} \rfloor = \lfloor nx \rfloor$
negative_passages.docid: 138072
negative_passages.text: Linear time algorithm for 2-SUM
negative_passages.docid: 98808
negative_passages.text: Finite Sum $\sum_{i=1}^n\frac i {2^i}$
negative_passages.docid: 68080
negative_passages.text: Evaluation of $\sum_{k=0}^n{n\choose k}^2u^k$
negative_passages.docid: 63071
negative_passages.text: the least possible value for :$ \lfloor \frac{a+b}{c}\rfloor +\lfloor \frac{b+c}{a} \rfloor+\lfloor \frac{c+a}{b} \rfloor $
negative_passages.docid: 40779
negative_passages.text: What is the smallest possible value of $\lfloor (a+b+c)/d\rfloor+\lfloor (a+b+d)/c\rfloor+\lfloor (a+d+c)/b\rfloor+\lfloor (d+b+c)/a\rfloor$?
negative_passages.docid: 65715
negative_passages.text: Distribution of sums
negative_passages.docid: 55777
negative_passages.text: A tricky sum to infinity
negative_passages.docid: 14884
negative_passages.text: Compute a sum with partial fraction decomposition and generating functions
negative_passages.docid: 96585
negative_passages.text: Sums and permutation
negative_passages.docid: 48092
negative_passages.text: Inequality involving a finite sum
negative_passages.docid: 151012
negative_passages.text: Find the value of $\lfloor x+y \rfloor$ where $x \in \mathbb{R}$, $y \in \mathbb{Z}$
negative_passages.docid: 17285
negative_passages.text: Proof of greatest integer theorem: floor function is well-defined
negative_passages.docid: 37586
negative_passages.text: How to find $\sum_{i=1}^n\left\lfloor i\sqrt{2}\right\rfloor$ A001951 A Beatty sequence: a(n) = floor(n*sqrt(2)).
negative_passages.docid: 47923
negative_passages.text: For $n\in\mathbb{N}$, evaluate $\int_0^n \cos(2\pi \lfloor x\rfloor\{x\})dx$