Question

Proving $\lfloor na_n \rfloor = 0$ if $a_n > 0$ and $a_n^2<a_n-a_{n+1}$

score 56 · Answer 1 · 2020-02-18 18:45:19

56

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Proving $\lfloor na_n \rfloor = 0$ if $a_n > 0$ and $a_n^2<a_n-a_{n+1}$

Published on 18 Feb 2020 - 18:45

score 123 · Answer 2 · 2020-02-18 20:30:06

123

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Equation with inverse trigonometric functions and logarithms

Published on 18 Feb 2020 - 20:30

score 58 · Answer 3 · 2020-02-19 21:53:02

58

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Find $\left\lfloor \sum_{k=1}^n\sqrt[2k+1]{\frac{2k+1}{2k-1}}\right\rfloor$

Published on 19 Feb 2020 - 21:53

score 143 · Answer 4 · 2020-02-20 20:45:52

143

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A $p$-congruence involving binomial coefficients and the floor function.

Published on 20 Feb 2020 - 20:45

score 49 · Answer 5 · 2020-02-23 02:13:30

49

Views

Graphing sum of floor functions

Published on 23 Feb 2020 - 2:13

score 71 · Answer 6 · 2020-02-24 18:16:29

71

Views

Solving $\lfloor \sqrt{9n^2+1}\rfloor+\lfloor\sqrt{9n^2+2}\rfloor+...+\lfloor\sqrt{9n^2+24n}\rfloor=349 $

Published on 24 Feb 2020 - 18:16

score 192 · Answer 7 · 2020-02-27 18:19:40

192

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integer part of the number

Published on 27 Feb 2020 - 18:19

score 104 · Answer 8 · 2026-03-26 16:06:16

104

Views

Find $\lfloor k^4\rfloor$ where $k^3 - 5k^2 + 2 = 0$.

Published on 26 Mar 2026 - 16:06

score 67 · Answer 9 · 2020-03-05 11:40:25

67

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Inequality proof problem

Published on 05 Mar 2020 - 11:40

score 117 · Answer 10 · 2020-03-06 06:11:49

117

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Antiderivative of $\lfloor\frac{2}{1+x^2}\rfloor$

Published on 06 Mar 2020 - 6:11

score 193 · Answer 11 · 2020-03-08 13:50:20

193

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At least one even number among $\{ \lfloor 2^{n}\sqrt{2} \rfloor, \lfloor 2^{n+1}\sqrt{2} \rfloor,..., \lfloor 2^{2n}\sqrt{2} \rfloor \}$

Published on 08 Mar 2020 - 13:50

score 621 · Answer 12 · 2026-03-28 09:57:37

621

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Prove that $\left\lfloor{\frac{n}{2}}\right\rfloor+\left\lfloor\frac{\left\lceil\frac{n}{2}\right\rceil}{2}\right\rfloor+\cdots=n-1$.

Published on 28 Mar 2026 - 9:57

score 120 · Answer 13 · 2026-03-25 19:07:14

120

Views

Unexpected result, does $\Big\lfloor\frac{n-1}{2}\Big\rfloor=\sum_{i=1}^\infty\bigg\lfloor\frac{n+2^i-1}{2^{i+1}}\bigg\rfloor $

Published on 25 Mar 2026 - 19:07

score 92 · Answer 14 · 2026-03-25 13:58:08

92

Views

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 25 Mar 2026 - 13:58

score 189 · Answer 15 · 2026-03-25 13:54:46

189

Views

Upper bound on summation involving fractional part

Published on 25 Mar 2026 - 13:54

List Question

Proving $\lfloor na_n \rfloor = 0$ if $a_n > 0$ and $a_n^2<a_n-a_{n+1}$

Equation with inverse trigonometric functions and logarithms

Find $\left\lfloor \sum_{k=1}^n\sqrt[2k+1]{\frac{2k+1}{2k-1}}\right\rfloor$

A $p$-congruence involving binomial coefficients and the floor function.

Graphing sum of floor functions

Solving $\lfloor \sqrt{9n^2+1}\rfloor+\lfloor\sqrt{9n^2+2}\rfloor+...+\lfloor\sqrt{9n^2+24n}\rfloor=349 $

integer part of the number

Find $\lfloor k^4\rfloor$ where $k^3 - 5k^2 + 2 = 0$.

Inequality proof problem

Antiderivative of $\lfloor\frac{2}{1+x^2}\rfloor$

At least one even number among $\{ \lfloor 2^{n}\sqrt{2} \rfloor, \lfloor 2^{n+1}\sqrt{2} \rfloor,..., \lfloor 2^{2n}\sqrt{2} \rfloor \}$

Prove that $\left\lfloor{\frac{n}{2}}\right\rfloor+\left\lfloor\frac{\left\lceil\frac{n}{2}\right\rceil}{2}\right\rfloor+\cdots=n-1$.

Unexpected result, does $\Big\lfloor\frac{n-1}{2}\Big\rfloor=\sum_{i=1}^\infty\bigg\lfloor\frac{n+2^i-1}{2^{i+1}}\bigg\rfloor $

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

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