query: How to prove this property involving 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: 53767
negative_passages.text: How to prove that derivatives have the Intermediate Value Property
negative_passages.docid: 96791
negative_passages.text: How to show that $\lfloor n/1\rfloor+\lfloor n/2 \rfloor+....+\lfloor n/n\rfloor+\lfloor{\sqrt{n}}\rfloor$ is even?
negative_passages.docid: 2251
negative_passages.text: Can someone give me a hint on how to prove this?
negative_passages.docid: 138316
negative_passages.text: A simple inequality for floor function
negative_passages.docid: 59872
negative_passages.text: How to prove $\inf(S)=-\sup(-S)$?
negative_passages.docid: 101641
negative_passages.text: Induction with floor, ceiling $n\le2^k\implies a_n\le3\cdot k2^k+4\cdot2^k-1$ for $a_n=a_{\lfloor\frac{n}2\rfloor}+a_{\lceil\frac{n}2\rceil}+3n+1$
negative_passages.docid: 120600
negative_passages.text: Real analysis derivate problem. How can I prove this?
negative_passages.docid: 114889
negative_passages.text: Solve summation $\sum_{i=1}^n \lfloor e\cdot i \rfloor $
negative_passages.docid: 38811
negative_passages.text: Solutions to $\frac1{\lfloor x\rfloor}+\frac1{\lfloor 2x\rfloor}=\{x\}+\frac13$
negative_passages.docid: 82803
negative_passages.text: Prove that $\lfloor\lfloor x/2 \rfloor / 2 \rfloor = \lfloor x/4 \rfloor$
negative_passages.docid: 99483
negative_passages.text: If $T(n+1)=T(n)+\lfloor \sqrt{n+1}, \rfloor$ $\forall n\geq 1$, what is $T(m^2)$?
negative_passages.docid: 45480
negative_passages.text: Does $\sum\frac{(-1)^{\lfloor \sqrt n\rfloor}}{ n}$ converge?
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: 77973
negative_passages.text: How to prove or disprove $\forall x\in\Bbb{R}, \forall n\in\Bbb{N},n\gt 0\implies \lfloor\frac{\lfloor x\rfloor}{n}\rfloor=\lfloor\frac{x}{n}\rfloor$.
negative_passages.docid: 130722
negative_passages.text: Can you prove this property?
negative_passages.docid: 117262
negative_passages.text: Proving a logarithm inequality