Question

$\lfloor\frac12+\frac1{2^2}+\frac1{2^3}+\cdots\rfloor\;$ vs $\;\lim_{n\to\infty}\lfloor\frac12+\frac1{2^2}+\cdots+\frac1{2^n}\rfloor$

score 181 · Answer 1 · 2020-07-16 14:54:21

181

Views

$\lfloor\frac12+\frac1{2^2}+\frac1{2^3}+\cdots\rfloor\;$ vs $\;\lim_{n\to\infty}\lfloor\frac12+\frac1{2^2}+\cdots+\frac1{2^n}\rfloor$

Published on 16 Jul 2020 - 14:54

score 103 · Answer 2 · 2020-07-18 00:59:43

103

Views

Motivation confusion in floor and ceiling function algebra

Published on 18 Jul 2020 - 0:59

score 225 · Answer 3 · 2020-07-19 15:33:20

225

Views

Does $\int_0^{\pi \over 2} \lfloor \tan(x) \rfloor\, dx$ converge?

Published on 19 Jul 2020 - 15:33

score 186 · Answer 4 · 2020-07-20 15:56:17

186

Views

Inequalities related to ceil function

Published on 20 Jul 2020 - 15:56

score 58 · Answer 5 · 2020-07-22 07:57:55

58

Views

proof involving floor functions

Published on 22 Jul 2020 - 7:57

score 37 · Answer 6 · 2026-03-25 18:49:53

37

Views

Can closed forms for the outputs in this production simulation be found?

Published on 25 Mar 2026 - 18:49

score 190 · Answer 7 · 2020-07-23 10:13:51

190

Views

Solve $\lfloor \ln x \rfloor \gt \ln \lfloor x\rfloor$

Published on 23 Jul 2020 - 10:13

score 2.3k · Answer 8 · 2026-03-25 12:49:40

2.3k

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The number of ways to represent a natural number as the sum of three different natural numbers

Published on 25 Mar 2026 - 12:49

score 88 · Answer 9 · 2020-07-27 11:24:32

88

Views

Prove that $\sum_{r=2}^{n} \left \lfloor n^{\frac{1}{r}} \right \rfloor = \sum_{r=2}^{n} \left \lfloor \log_{r}(n) \right \rfloor$.

Published on 27 Jul 2020 - 11:24

score 295 · Answer 10 · 2016-07-06 01:42:08

295

Views

How to integrate the following floor function?

Published on 06 Jul 2016 - 1:42

score 1.2k · Answer 11 · 2016-07-06 15:11:20

Find the number of solutions to $ \lfloor x \rfloor + \lfloor 2x \rfloor + \lfloor 4x \rfloor + \ldots + \lfloor 32x \rfloor =12345$

score 100 · Answer 12 · 2016-07-06 17:16:51

100

Views

Evaluate the limit of $\frac{\sin \lfloor x+1\rfloor }{ \lfloor x+1\rfloor }$ at $x=-1$

Published on 06 Jul 2016 - 17:16

score 242 · Answer 13 · 2016-07-07 04:29:50

242

Views

Prove that $[\sqrt{n}+\sqrt{n+1}]=[\sqrt{4n+1}]$

Published on 07 Jul 2016 - 4:29

score 60 · Answer 14 · 2016-07-07 15:01:35

60

Views

Find the limit: $\lim_{n\to\infty} \frac{ \sum_{i=1}^n\lfloor i^3x \rfloor}{n^4}$

Published on 07 Jul 2016 - 15:01

score 454 · Answer 15 · 2016-07-08 07:49:55

454

Views

Necessary and sufficient condition that $ \lceil \sqrt { \lfloor x \rfloor } \rceil = \lceil \sqrt { x } \rceil $

Published on 08 Jul 2016 - 7:49

List Question

$\lfloor\frac12+\frac1{2^2}+\frac1{2^3}+\cdots\rfloor\;$ vs $\;\lim_{n\to\infty}\lfloor\frac12+\frac1{2^2}+\cdots+\frac1{2^n}\rfloor$

Motivation confusion in floor and ceiling function algebra

Does $\int_0^{\pi \over 2} \lfloor \tan(x) \rfloor\, dx$ converge?

Inequalities related to ceil function

proof involving floor functions

Can closed forms for the outputs in this production simulation be found?

Solve $\lfloor \ln x \rfloor \gt \ln \lfloor x\rfloor$

The number of ways to represent a natural number as the sum of three different natural numbers

Prove that $\sum_{r=2}^{n} \left \lfloor n^{\frac{1}{r}} \right \rfloor = \sum_{r=2}^{n} \left \lfloor \log_{r}(n) \right \rfloor$.

How to integrate the following floor function?

Find the number of solutions to $ \lfloor x \rfloor + \lfloor 2x \rfloor + \lfloor 4x \rfloor + \ldots + \lfloor 32x \rfloor =12345$

Evaluate the limit of $\frac{\sin \lfloor x+1\rfloor }{ \lfloor x+1\rfloor }$ at $x=-1$

Prove that $[\sqrt{n}+\sqrt{n+1}]=[\sqrt{4n+1}]$

Find the limit: $\lim_{n\to\infty} \frac{ \sum_{i=1}^n\lfloor i^3x \rfloor}{n^4}$

Necessary and sufficient condition that $ \lceil \sqrt { \lfloor x \rfloor } \rceil = \lceil \sqrt { x } \rceil $

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