New posts in Fractional Part

Evaluate the following integral $ \int_1^{\infty} \frac{\lbrace x\rbrace-\frac{1}2}{x} dx$

What is the behaviour of the first $n$ digits of ${\underbrace{99\dots99}_{n\text{ nines}}}^{\overbrace{99\dots99}^{n\text{ nines}}}$ as $n\to\infty$

Evaluate the limit $\lim\limits_{n\to0}\frac{(x)+(2x)+\cdots (nx)}{n^2}$

Evaluating $\liminf_{n\to\infty}n\{n\sqrt2\}$

Closed form of integral over fractional part $\int_0^1 \left\{\frac{1}{2}\left(x+\frac{1}{x}\right)\right\}\,dx$

Compute a division with integer and fractional part

Minimum values of the sequence $\{n\sqrt{2}\}$

$\int_{0<x<y<z<w<1} \left\{\frac{x}{y}\right\}\left\{\frac{y}{z}\right\}\left\{\frac{z}{w}\right\}\left\{\frac{w}{x}\right\}$

The equation $\{x^2\} + \{x\}=1$ has no solution over positive rationals

Evaluate $\int_0^1\int_0^1 \left\{ \frac{e^x}{e^y} \right\}dxdy$