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15
229
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On the convergence of $\sum\frac{\log(n)}{n}\{x^n+x^{-n}\}$

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#real-analysis #calculus #sequences-and-series #convergence-divergence #fractional-part
61
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Limit of the decimal part of $\sqrt{4n^2+38n}$

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#limits #fractional-part
237
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Limit of alternating sum of fractional parts

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#real-analysis #sequences-and-series #limits #fractional-part
151
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Find the asymptotic expansion as $N \rightarrow \infty$ of $\sum_{k=1}^{\left\lfloor{N/2}\right\rfloor} \left\{{\sqrt{{N}^{2}+{k}^{2}}}\right\}$

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#elementary-number-theory #asymptotics #divisor-sum #sums-of-squares #fractional-part
115
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What is the standard notation for the set of rationals with finite fractional part?

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#notation #rational-numbers #fractional-part
47
Views

Try to prove the inequality

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#sequences-and-series #fractional-part
218
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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 $n\to\infty$

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#number-theory #decimal-expansion #fractional-part
74
Views

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

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#sequences-and-series #fractional-part #equidistribution
92
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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 $x\in\Bbb R$.

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#algebra-precalculus #contest-math #problem-solving #ceiling-and-floor-functions #fractional-part
189
Views

Upper bound on summation involving fractional part

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#inequality #summation #ceiling-and-floor-functions #upper-lower-bounds #fractional-part
38
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Considering this constraint, determine the real function $f$

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#functional-equations #ceiling-and-floor-functions #fractional-part
83
Views

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

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#inequality #absolute-value #fractional-part
118
Views

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

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#integration #definite-integrals #fractional-part #telescopic-series #summation-by-parts
172
Views

Another double fractional part integral

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#integration #multivariable-calculus #definite-integrals #fractional-part
91
Views

Another even worse double fractional part integral

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#integration #multiple-integral #fractional-part

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