Newbetuts

How to prove floor function inequality $\sum\limits_{k=1}^{n}\frac{\{kx\}}{\lfloor kx\rfloor }<\sum\limits_{k=1}^{n}\frac{1}{2k-1}$ for $x>1$

$\lim_{n\to\infty}\frac{n -\big\lfloor\frac{n}{2}\big\rfloor+\big\lfloor\frac{n}{3}\big\rfloor-\dots}{n}$, a Brilliant problem

How do the floor and ceiling functions work on negative numbers?

How do I evaluate this sum(involving the floor function)? [duplicate]

Calculate the minimum value of an integer $x$, such that $\left\lfloor\frac{xy^2}{xy+w(y-z)}\right\rfloor>z$

Is $\lfloor{\frac{a+b+c+d}{4}}\rfloor=\lfloor\frac{\lfloor{\frac{a+b}{2}}\rfloor+\lfloor{\frac{c+d}{2}}\rfloor}{2}\rfloor$ for $a,b,c,d\in\mathbb R$?

How do we prove that $\lfloor0.999\cdots\rfloor = \lfloor 1 \rfloor$?

How to find $\sum_{i=1}^n\left\lfloor i\sqrt{2}\right\rfloor$ A001951 A Beatty sequence: a(n) = floor(n*sqrt(2)).

Proof of greatest integer theorem: floor function is well-defined

there exist infinite many $n\in\mathbb{N}$ such that $S_n-[S_n]<\frac{1}{n^2}$

Does this pattern continue $\lfloor\sqrt{44}\rfloor=6, \lfloor\sqrt{4444}\rfloor=66,\dots$?

$\lfloor \sqrt n+\sqrt {n+1}+\sqrt{n+2}+\sqrt{n+3}+\sqrt{n+4}\rfloor=\lfloor\sqrt {25n+49}\rfloor$ is true?

Identity involving Euler's totient function: $\sum \limits_{k=1}^n \left\lfloor \frac{n}{k} \right\rfloor \varphi(k) = \frac{n(n+1)}{2}$

Is there a "good" reason why $\left\lfloor \frac{n!}{11e}\right\rfloor$ is always even?

Is $\lfloor n!/e\rfloor$ always even for $n\in\mathbb N$?

How to solve an definite integral of floor valute function?

For $x\in\mathbb R\setminus\mathbb Q$, the set $\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$ is dense on $[0,1)$

New posts in ceiling-and-floor-functions

How to prove floor function inequality $\sum\limits_{k=1}^{n}\frac{\{kx\}}{\lfloor kx\rfloor }<\sum\limits_{k=1}^{n}\frac{1}{2k-1}$ for $x>1$

How to show $\lim_{n \to \infty} a_n = \frac{ [x] + [2x] + [3x] + \dotsb + [nx] }{n^2} = x/2$?

Solve summation $\sum_{i=1}^n \lfloor e\cdot i \rfloor $

Find a formula for $\sum\limits_{k=1}^n \lfloor \sqrt{k} \rfloor$

$\lim_{n\to\infty}\frac{n -\big\lfloor\frac{n}{2}\big\rfloor+\big\lfloor\frac{n}{3}\big\rfloor-\dots}{n}$, a Brilliant problem

How do the floor and ceiling functions work on negative numbers?

How do I evaluate this sum(involving the floor function)? [duplicate]

Calculate the minimum value of an integer $x$, such that $\left\lfloor\frac{xy^2}{xy+w(y-z)}\right\rfloor>z$

Is $\lfloor{\frac{a+b+c+d}{4}}\rfloor=\lfloor\frac{\lfloor{\frac{a+b}{2}}\rfloor+\lfloor{\frac{c+d}{2}}\rfloor}{2}\rfloor$ for $a,b,c,d\in\mathbb R$?

How do we prove that $\lfloor0.999\cdots\rfloor = \lfloor 1 \rfloor$?

How to find $\sum_{i=1}^n\left\lfloor i\sqrt{2}\right\rfloor$ A001951 A Beatty sequence: a(n) = floor(n*sqrt(2)).

Proof of greatest integer theorem: floor function is well-defined

there exist infinite many $n\in\mathbb{N}$ such that $S_n-[S_n]<\frac{1}{n^2}$

Does this pattern continue $\lfloor\sqrt{44}\rfloor=6, \lfloor\sqrt{4444}\rfloor=66,\dots$?

$\lfloor \sqrt n+\sqrt {n+1}+\sqrt{n+2}+\sqrt{n+3}+\sqrt{n+4}\rfloor=\lfloor\sqrt {25n+49}\rfloor$ is true?

Identity involving Euler's totient function: $\sum \limits_{k=1}^n \left\lfloor \frac{n}{k} \right\rfloor \varphi(k) = \frac{n(n+1)}{2}$

Is there a "good" reason why $\left\lfloor \frac{n!}{11e}\right\rfloor$ is always even?

Is $\lfloor n!/e\rfloor$ always even for $n\in\mathbb N$?

How to solve an definite integral of floor valute function?

For $x\in\mathbb R\setminus\mathbb Q$, the set $\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$ is dense on $[0,1)$