List questions from fractional-part

Published on 21 Oct 2020 - 13:09

401

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Sum of fractional parts

Published on 24 Oct 2020 - 12:11

199

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Asymptotic estimate as $N \rightarrow \infty$ of $\sum\limits_{n = 1}^{N} \left\{{\frac{\left({n \pm 1}\right)}{{n}^{2}} N}\right\}$

Published on 07 Nov 2020 - 22:20

127

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How to prove that frac($\sqrt{4^n-1}$) is greater than 1/2 for any natural n

Published on 09 Nov 2020 - 19:08

160

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Series of integer part using fractionnal part fourrier series

Published on 28 Mar 2026 - 12:02

15

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Simplification of complex rational?

Published on 04 Mar 2026 - 7:03

85

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Apply the method of hyperpolas to $\sum_{n \le {x}^{1/k}} n * Fraction \left(\frac{x}{{n}^{k}}\right)$

Published on 26 Mar 2026 - 3:01

270

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Find a closed form for the following integral:

Published on 27 Dec 2020 - 13:30

71

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{$\frac{1}{x}$} , $0<x\leq1$ in terms of {$x$}, $x\geq 1$, {$x$} is fractional part of $x$

Published on 29 Dec 2020 - 7:51

459

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A possible upper bound on the fractional part of exponential functions

Published on 09 Jan 2021 - 11:32

353

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Sum of two floors is equal

Published on 11 Jan 2021 - 10:29

97

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Solve ${x}^{\lfloor x \rfloor} = a$

Published on 25 Feb 2021 - 8:09

112

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Finding all rational values of $x$ for which $256(x + 15\{x\})\{x\} = 2021$

Published on 17 Mar 2021 - 19:31

52

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Does $\lim_{k\to\infty}2^k \log_2(2^k-1)\equiv\gamma\mod 1$ where $k\in\mathbb{N}$ (Euler-Mascheroni Constant)

Published on 27 Mar 2026 - 0:04

49

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Infinitely recursive summation of floor function

Published on 14 May 2021 - 13:10

List Question

Integral representation of $\zeta(s)$ in terms of the fractional part of $x$

Sum of fractional parts

Asymptotic estimate as $N \rightarrow \infty$ of $\sum\limits_{n = 1}^{N} \left\{{\frac{\left({n \pm 1}\right)}{{n}^{2}} N}\right\}$

How to prove that frac($\sqrt{4^n-1}$) is greater than 1/2 for any natural n

Series of integer part using fractionnal part fourrier series

Simplification of complex rational?

Apply the method of hyperpolas to $\sum_{n \le {x}^{1/k}} n * Fraction \left(\frac{x}{{n}^{k}}\right)$

Find a closed form for the following integral:

{$\frac{1}{x}$} , $0<x\leq1$ in terms of {$x$}, $x\geq 1$, {$x$} is fractional part of $x$

A possible upper bound on the fractional part of exponential functions

Sum of two floors is equal

Solve ${x}^{\lfloor x \rfloor} = a$

Finding all rational values of $x$ for which $256(x + 15\{x\})\{x\} = 2021$

Does $\lim_{k\to\infty}2^k \log_2(2^k-1)\equiv\gamma\mod 1$ where $k\in\mathbb{N}$ (Euler-Mascheroni Constant)

Infinitely recursive summation of floor function

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