Question

Inequality involving floor function

score 168 · Answer 1 · 2017-01-15 02:15:45

168

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Inequality involving floor function

Published on 15 Jan 2017 - 2:15

score 42 · Answer 2 · 2017-01-15 14:17:03

42

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Are these function cases at all equivalent?

Published on 15 Jan 2017 - 14:17

score 50 · Answer 3 · 2017-01-16 21:58:47

50

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$\lfloor x^2 +2x +7/4\rfloor =k ,\lfloor x^2 +x +7/2\rfloor=n$

Published on 16 Jan 2017 - 21:58

score 58 · Answer 4 · 2026-03-28 15:21:13

58

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If $n>1$ is a power of $2$, show that $H_n \le 1 + \lceil{\log_2(n)}\rceil$ where $H_n$ denotes the $n^{th}$ harmonic number

Published on 28 Mar 2026 - 15:21

score 354 · Answer 5 · 2017-01-17 09:25:18

354

Views

Limit $\lim_{x \to 0} \frac{\sin[x]}{[x]}$

Published on 17 Jan 2017 - 9:25

score 220 · Answer 6 · 2017-01-18 16:56:52

220

Views

Finding $\lim_{x\rightarrow 0}\lfloor \frac{2017 \sin x}{x} \rfloor +\lfloor \frac{2017 \tan x}{x} \rfloor $

Published on 18 Jan 2017 - 16:56

score 87 · Answer 7 · 2017-01-20 01:51:05

87

Views

Value of the integral $\int_1^\infty \frac{\lfloor x\rfloor}{x^3} \, dx$

Published on 20 Jan 2017 - 1:51

score 80 · Answer 8 · 2017-01-21 00:30:04

80

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Limit $\lim_{x \rightarrow ( -\frac{1}{10} )^-} [ \frac{1}{x} ]=?$

Published on 21 Jan 2017 - 0:30

score 153 · Answer 9 · 2017-01-22 03:14:36

153

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Prove $\sum_{k=1}^\infty\left \lfloor{\frac{n}{p^k}}\right\rfloor \leq 2\sum_{k=1}^\infty\left \lfloor{\frac{n-1}{p^k}}\right\rfloor$

Published on 22 Jan 2017 - 3:14

score 312 · Answer 10 · 2017-01-25 16:16:56

312

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Analyzing $\biggl\lfloor{\frac{x}{5}}\bigg\rfloor=\bigg\lfloor{\frac{x}{7}}\bigg\rfloor$

Published on 25 Jan 2017 - 16:16

score 87 · Answer 11 · 2017-01-27 03:35:32

87

Views

Solving: $\sum\limits_{k=3}^{n}\bigg\lfloor | \frac {-1-\sqrt {1+8k}} {2}|\bigg\rfloor$

Published on 27 Jan 2017 - 3:35

score 246 · Answer 12 · 2017-01-27 19:48:31

246

Views

When I was solving an equation with floor function in my class

Published on 27 Jan 2017 - 19:48

score 71 · Answer 13 · 2017-01-29 17:50:19

71

Views

Evaluating the floor of a tough looking summation

Published on 29 Jan 2017 - 17:50

score 396 · Answer 14 · 2017-02-02 01:28:35

396

Views

When does $\left\lfloor\sqrt{2015(n-1)}\right\rfloor = \left\lfloor\sqrt{2015n}\right\rfloor$ hold?

Published on 02 Feb 2017 - 1:28

score 493 · Answer 15 · 2017-02-03 03:14:04

493

Views

Does anyone know how to reduce this sum of sums into something simpler in order to find a special value?

Published on 03 Feb 2017 - 3:14

List Question

Inequality involving floor function

Are these function cases at all equivalent?

$\lfloor x^2 +2x +7/4\rfloor =k ,\lfloor x^2 +x +7/2\rfloor=n$

If $n>1$ is a power of $2$, show that $H_n \le 1 + \lceil{\log_2(n)}\rceil$ where $H_n$ denotes the $n^{th}$ harmonic number

Limit $\lim_{x \to 0} \frac{\sin[x]}{[x]}$

Finding $\lim_{x\rightarrow 0}\lfloor \frac{2017 \sin x}{x} \rfloor +\lfloor \frac{2017 \tan x}{x} \rfloor $

Value of the integral $\int_1^\infty \frac{\lfloor x\rfloor}{x^3} \, dx$

Limit $\lim_{x \rightarrow ( -\frac{1}{10} )^-} [ \frac{1}{x} ]=?$

Prove $\sum_{k=1}^\infty\left \lfloor{\frac{n}{p^k}}\right\rfloor \leq 2\sum_{k=1}^\infty\left \lfloor{\frac{n-1}{p^k}}\right\rfloor$

Analyzing $\biggl\lfloor{\frac{x}{5}}\bigg\rfloor=\bigg\lfloor{\frac{x}{7}}\bigg\rfloor$

Solving: $\sum\limits_{k=3}^{n}\bigg\lfloor | \frac {-1-\sqrt {1+8k}} {2}|\bigg\rfloor$

When I was solving an equation with floor function in my class

Evaluating the floor of a tough looking summation

When does $\left\lfloor\sqrt{2015(n-1)}\right\rfloor = \left\lfloor\sqrt{2015n}\right\rfloor$ hold?

Does anyone know how to reduce this sum of sums into something simpler in order to find a special value?

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