Newbetuts

The units digit of $1!+2!+3!+4!!+5!!+\dots+k\underset{\left \lfloor \sqrt{k} \right \rfloor \text{ times}}{\underbrace{!!!\dots!}}$

$\lfloor a n\rfloor \lfloor b n\rfloor \lfloor c n\rfloor = \lfloor d n\rfloor \lfloor e n\rfloor \lfloor f n\rfloor$ for all $n$

Condition that satisfies inequality involving fractions and the floor function

What is the smallest possible value of $\lfloor (a+b+c)/d\rfloor+\lfloor (a+b+d)/c\rfloor+\lfloor (a+d+c)/b\rfloor+\lfloor (d+b+c)/a\rfloor$?

Are ceiling and floor elementary functions?

prove that $\lfloor x\rfloor\lfloor y\rfloor\le\lfloor xy\rfloor$

Explicit formula for floor(x)?

Calculate the sum $S_n = \sum\limits_{k=1}^{\infty}\left\lfloor \frac{n}{2^k} + \frac{1}{2}\right\rfloor $

Solve the equation $\lfloor x^2\rfloor-3\lfloor x \rfloor +2=0$

Is it true that $\left\lfloor\sum_{s=1}^n\operatorname{Li}_s\left(\frac 1k \right)\right\rfloor\stackrel{?}{=}\left\lfloor\frac nk \right\rfloor$

Floor equation $x=\frac{⌊x⌋}{x - ⌊x⌋}$

Find $\lim_{n\rightarrow \infty}\left(\sqrt{n^2+n+1}-\big\lfloor \sqrt{n^2+n+1} \big\rfloor \right)$

$20\{x\} = x + [x] + [x + 0.5]$

Prove the following ceiling and floor identities?

find positive real number x that satisfies $2001=x\lfloor x\lfloor x\lfloor x\rfloor\rfloor\rfloor$

How do we solve $x^2 + \{x\}^2 = 33$ without computer?

Solve for $x$ in the equation containing ${\lfloor{x}\rfloor}$ and $\{x\}$

Find the real values of $x$ that satisfy the equation $7[x]+23\{x\}=191$

New posts in ceiling-and-floor-functions

The units digit of $1!+2!+3!+4!!+5!!+\dots+k\underset{\left \lfloor \sqrt{k} \right \rfloor \text{ times}}{\underbrace{!!!\dots!}}$

Compare $\sum_{k=1}^n \left\lfloor \frac{k}{\varphi}\right\rfloor$ ...

Integral of a floor function.

$\lfloor a n\rfloor \lfloor b n\rfloor \lfloor c n\rfloor = \lfloor d n\rfloor \lfloor e n\rfloor \lfloor f n\rfloor$ for all $n$

Condition that satisfies inequality involving fractions and the floor function

What is the smallest possible value of $\lfloor (a+b+c)/d\rfloor+\lfloor (a+b+d)/c\rfloor+\lfloor (a+d+c)/b\rfloor+\lfloor (d+b+c)/a\rfloor$?

Are ceiling and floor elementary functions?

prove that $\lfloor x\rfloor\lfloor y\rfloor\le\lfloor xy\rfloor$

Explicit formula for floor(x)?

Calculate the sum $S_n = \sum\limits_{k=1}^{\infty}\left\lfloor \frac{n}{2^k} + \frac{1}{2}\right\rfloor $

Solve the equation $\lfloor x^2\rfloor-3\lfloor x \rfloor +2=0$

Is it true that $\left\lfloor\sum_{s=1}^n\operatorname{Li}_s\left(\frac 1k \right)\right\rfloor\stackrel{?}{=}\left\lfloor\frac nk \right\rfloor$

Floor equation $x=\frac{⌊x⌋}{x - ⌊x⌋}$

Find $\lim_{n\rightarrow \infty}\left(\sqrt{n^2+n+1}-\big\lfloor \sqrt{n^2+n+1} \big\rfloor \right)$

$20\{x\} = x + [x] + [x + 0.5]$

Prove the following ceiling and floor identities?

find positive real number x that satisfies $2001=x\lfloor x\lfloor x\lfloor x\rfloor\rfloor\rfloor$

How do we solve $x^2 + \{x\}^2 = 33$ without computer?

Solve for $x$ in the equation containing ${\lfloor{x}\rfloor}$ and $\{x\}$

Find the real values of $x$ that satisfy the equation $7[x]+23\{x\}=191$