Newbetuts

Find $\sum_{n=1}^\infty\frac{2^{f(n)}+2^{-f(n)}}{2^n}$, where $f(n)=\left[\sqrt n +\frac 12\right]$ denotes greatest integer function

Find the limit $\lim_{n\to\infty}\left(\sqrt{n^2+n+1}-\left\lfloor\sqrt{n^2+n+1}\right\rfloor\right)$ [duplicate]

Number of real solutions of $\begin{array}{r} {\left[\frac{2 x+1}{3}\right]+\left[\frac{4 x+5}{6}\right]} =\frac{3 x-1}{2} \end{array}$

Struggling to solve an equation containing a floor function

$\lfloor (2+\sqrt{3})^n \rfloor $ is odd

Prove integer remains $\mathbb{Z}_{n}$ after Division and Floor

$\lfloor (25x-2)/4 \rfloor =(13x+4)/3$

Detailed analysis of the secretary problem

Closed expression for sum $\sum_{k=1}^{\infty} (-1)^{k+1}\frac{\left\lfloor \sqrt{k}\right\rfloor}{k}$

Integral of floor function: $\int \,\left\lfloor\frac{1}{x}\right\rfloor\, dx$

Explicit solution of the recursion $x_n = x_{n-1}^2 - 2$ with $x_0>2$

MCQ (No Calculators): What is the remainder when dividing $\left \lfloor (6+\sqrt{7})^8 \right \rfloor$ by $9$?

How to prove $\left \lceil \frac{n}{m} \right \rceil = \left \lfloor \frac{n+m-1}{m} \right \rfloor$?

finding big omega of $n^k$ by splitting the sum (big-$O$ notation)

Proving $\sum\limits_{k=0}^{n-1} \Bigl[x + \frac{k}{n}\Bigr] = [nx]$ [duplicate]

New posts in ceiling-and-floor-functions

Solve the equation $7t+[2t] =52 $ ,where $[x]$ denotes the floor function for $x$.

If $x\in\mathbb R$, solve $4x^2-40\lfloor x\rfloor+51=0$.

Solve $\lfloor \sqrt x +\sqrt{x+1}+\sqrt{x+2}\rfloor=x$

Continuity of composition of root and floor function

Solving $7[x]+23\{x\}=191$

Find $\sum_{n=1}^\infty\frac{2^{f(n)}+2^{-f(n)}}{2^n}$, where $f(n)=\left[\sqrt n +\frac 12\right]$ denotes greatest integer function

Find the limit $\lim_{n\to\infty}\left(\sqrt{n^2+n+1}-\left\lfloor\sqrt{n^2+n+1}\right\rfloor\right)$ [duplicate]

Number of real solutions of $\begin{array}{r} {\left[\frac{2 x+1}{3}\right]+\left[\frac{4 x+5}{6}\right]} =\frac{3 x-1}{2} \end{array}$

Struggling to solve an equation containing a floor function

$\lfloor (2+\sqrt{3})^n \rfloor $ is odd

Prove integer remains $\mathbb{Z}_{n}$ after Division and Floor

$\lfloor (25x-2)/4 \rfloor =(13x+4)/3$

Detailed analysis of the secretary problem

Closed expression for sum $\sum_{k=1}^{\infty} (-1)^{k+1}\frac{\left\lfloor \sqrt{k}\right\rfloor}{k}$

Integral of floor function: $\int \,\left\lfloor\frac{1}{x}\right\rfloor\, dx$

Explicit solution of the recursion $x_n = x_{n-1}^2 - 2$ with $x_0>2$

MCQ (No Calculators): What is the remainder when dividing $\left \lfloor (6+\sqrt{7})^8 \right \rfloor$ by $9$?

How to prove $\left \lceil \frac{n}{m} \right \rceil = \left \lfloor \frac{n+m-1}{m} \right \rfloor$?

finding big omega of $n^k$ by splitting the sum (big-$O$ notation)

Proving $\sum\limits_{k=0}^{n-1} \Bigl[x + \frac{k}{n}\Bigr] = [nx]$ [duplicate]