List questions from fractional-part

Published on 04 Jan 2020 - 11:02

60

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Limit of the decimal part of $\sqrt{4n^2+38n}$

Published on 06 Jan 2020 - 4:06

236

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Limit of alternating sum of fractional parts

Published on 15 Jan 2020 - 13:44

150

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Find the asymptotic expansion as $N \rightarrow \infty$ of $\sum_{k=1}^{\left\lfloor{N/2}\right\rfloor} \left\{{\sqrt{{N}^{2}+{k}^{2}}}\right\}$

Published on 20 Jan 2020 - 20:28

114

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What is the standard notation for the set of rationals with finite fractional part?

Published on 08 Feb 2020 - 12:31

45

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Try to prove the inequality

Published on 08 Feb 2020 - 19:10

217

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

Published on 12 Feb 2020 - 0:32

71

Views

On the convergence rate of $\sum \frac{\ln(n)}{n}\{x^n+x^{-n}\}$

Published on 25 Mar 2026 - 11:16

91

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Find all real numbers $a$ s.t. $\sum_{k=0}^{2019}\left\lfloor x+\frac{k}{a}\right\rfloor=\lfloor ax\rfloor$ for every $x\in\Bbb R$.

Published on 12 Mar 2020 - 10:09

188

Views

Upper bound on summation involving fractional part

Published on 21 Mar 2020 - 19:06

37

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Considering this constraint, determine the real function $f$

Published on 27 Mar 2020 - 8:10

82

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Show that $|\{x\}^2-\{x\}+1/6|\leq \frac{1}{6}$

Published on 09 Apr 2020 - 23:02

116

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Evaluating $\int_0^n \{x^2\}\,\text{d}x$

Published on 26 Feb 2026 - 3:22

171

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Another double fractional part integral

Published on 13 Apr 2020 - 21:02

90

Views

Another even worse double fractional part integral

Published on 15 Apr 2020 - 7:16

List Question

On the convergence of $\sum\frac{\log(n)}{n}\{x^n+x^{-n}\}$

Limit of the decimal part of $\sqrt{4n^2+38n}$

Limit of alternating sum of fractional parts

Find the asymptotic expansion as $N \rightarrow \infty$ of $\sum_{k=1}^{\left\lfloor{N/2}\right\rfloor} \left\{{\sqrt{{N}^{2}+{k}^{2}}}\right\}$

What is the standard notation for the set of rationals with finite fractional part?

Try to prove the inequality

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

On the convergence rate of $\sum \frac{\ln(n)}{n}\{x^n+x^{-n}\}$

Find all real numbers $a$ s.t. $\sum_{k=0}^{2019}\left\lfloor x+\frac{k}{a}\right\rfloor=\lfloor ax\rfloor$ for every $x\in\Bbb R$.

Upper bound on summation involving fractional part

Considering this constraint, determine the real function $f$

Show that $|\{x\}^2-\{x\}+1/6|\leq \frac{1}{6}$

Evaluating $\int_0^n \{x^2\}\,\text{d}x$

Another double fractional part integral

Another even worse double fractional part integral

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