query: Summation with the Floor function
positive_passages.docid: 1449
positive_passages.text: Floor function properties: $[2x] = [x] + [ x + \frac12 ]$ and $[nx] = \sum_{k = 0}^{n - 1} [ x + \frac{k}{n} ] $
negative_passages.docid: 29190
negative_passages.text: $\left\lfloor \frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{4}}+...+\frac{1}{\sqrt{1024}}\right\rfloor =?$
negative_passages.docid: 54521
negative_passages.text: Making all row sums and column sums non-negative by a sequence of moves
negative_passages.docid: 113237
negative_passages.text: Find the sum of the roots of the floor equation
negative_passages.docid: 10827
negative_passages.text: Writting a proof for $\lfloor 4x \rfloor = \lfloor x+1/4 \rfloor + \lfloor x+1/2 \rfloor + \lfloor x+3/4 \rfloor + \lfloor x \rfloor$
negative_passages.docid: 108694
negative_passages.text: Efficient computation of $\sum_{i=1}^{i=\left \lfloor {\sqrt{N}} \right \rfloor}\left \lfloor \frac{N}{i^{2}} \right \rfloor$
negative_passages.docid: 17285
negative_passages.text: Proof of greatest integer theorem: floor function is well-defined
negative_passages.docid: 27001
negative_passages.text: How to calculate the following sum:
negative_passages.docid: 130945
negative_passages.text: Summation using residues
negative_passages.docid: 125981
negative_passages.text: Closed-Form Solution to Infinite Sum
negative_passages.docid: 142338
negative_passages.text: Prove that $\lfloor\frac{n+1}{2}\rfloor+\lfloor\frac{n+2}{4}\rfloor+\lfloor\frac{n+4}{8}\rfloor+\lfloor\frac{n+8}{16}\rfloor+ \dots=n$
negative_passages.docid: 59327
negative_passages.text: How can I use sum() function for a list in Python?
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: 79836
negative_passages.text: Proof for $\left\lfloor\frac 1j\left\lfloor\frac nk\right\rfloor\right\rfloor=\left\lfloor\frac n{jk}\right\rfloor$
negative_passages.docid: 31478
negative_passages.text: Using bitwise OR 0 to floor a number
negative_passages.docid: 124426
negative_passages.text: Help in evaluating: $\lim_{n \to \infty} \frac{\sum_{k=1}^n\lfloor kx\rfloor}{n^2} $
negative_passages.docid: 45480
negative_passages.text: Does $\sum\frac{(-1)^{\lfloor \sqrt n\rfloor}}{ n}$ converge?