Question

What's the limit of the sequence $a_{n} = \frac{\lfloor\sqrt{2n}\rfloor}{\lfloor\sqrt{n}\rfloor}$?

score 68 · Answer 1 · 2023-11-28 14:53:27

68

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What's the limit of the sequence $a_{n} = \frac{\lfloor\sqrt{2n}\rfloor}{\lfloor\sqrt{n}\rfloor}$?

Published on 28 Nov 2023 - 14:53

score 57 · Answer 2 · 2023-12-04 18:32:02

57

Views

Find the limit of the function below

Published on 04 Dec 2023 - 18:32

score 39 · Answer 3 · 2026-02-25 05:52:23

39

Views

limit of the integral $\int_0^A \frac{1}{n!} [\log(\frac Bx)]^n~dx$ where $A,B$ are positive constants

Published on 25 Feb 2026 - 5:52

score 89 · Answer 4 · 2023-12-11 21:46:17

89

Views

$\int_0^x\frac{\lfloor t\rfloor}{t^2}dt=H_x$ isn't true?

Published on 11 Dec 2023 - 21:46

score 80 · Answer 5 · 2023-12-16 03:00:22

80

Views

Find the last two digits of the expression $\Bigl\lfloor \frac{10^{2001}}{10^{29}-2} \Bigr\rfloor$

Published on 16 Dec 2023 - 3:00

score 57 · Answer 6 · 2023-12-22 19:04:11

57

Views

Spotting error in this solution: Solve for $x : [x] -2x= 4$

Published on 22 Dec 2023 - 19:04

score 64 · Answer 7 · 2023-12-26 19:03:54

64

Views

Differentiable analogue of greatest integer (a.k.a. floor) function

Published on 26 Dec 2023 - 19:03

score 66 · Answer 8 · 2023-12-28 00:06:13

66

Views

Difference of consecutive square floor functions.

Published on 28 Dec 2023 - 0:06

score 87 · Answer 9 · 2023-12-29 17:24:24

87

Views

discrete math (functions that include ceiling and floor

Published on 29 Dec 2023 - 17:24

score 187 · Answer 10 · 2026-02-23 13:38:40

187

Views

Can the sequence $\{\lfloor \alpha n \rfloor\}$ be divided into two parts with equal sums, for all $\alpha \in \mathbb{R}$?

Published on 23 Feb 2026 - 13:38

score 96 · Answer 11 · 2024-01-01 17:01:45

96

Views

Proving that $\int_a^b\frac1{\lfloor x\rfloor}\;\mathrm{d}x$ is irrational, given $b - a$ is irrational

Published on 01 Jan 2024 - 17:01

score 197 · Answer 12 · 2026-03-27 16:21:53

197

Views

Vietnam Mathematical Olympiad 2024 - First Question

Published on 27 Mar 2026 - 16:21

score 51 · Answer 13 · 2024-01-05 18:05:41

51

Views

Query Regarding Equation Solution and Floor Functions

Published on 05 Jan 2024 - 18:05

score 48 · Answer 14 · 2024-01-09 20:28:33

48

Views

Solve in real $x,\,\,\lfloor x^3\rfloor-3\lfloor x^2\rfloor+2\lfloor x\rfloor=0$

Published on 09 Jan 2024 - 20:28

score 161 · Answer 15 · 2026-03-29 10:08:48

161

Views

Why must $n-\lfloor\frac n2\rfloor+\lfloor\frac n3\rfloor-\dotsb$ grow like $n\ln2$?

Published on 29 Mar 2026 - 10:08

List Question

What's the limit of the sequence $a_{n} = \frac{\lfloor\sqrt{2n}\rfloor}{\lfloor\sqrt{n}\rfloor}$?

Find the limit of the function below

limit of the integral $\int_0^A \frac{1}{n!} [\log(\frac Bx)]^n~dx$ where $A,B$ are positive constants

$\int_0^x\frac{\lfloor t\rfloor}{t^2}dt=H_x$ isn't true?

Find the last two digits of the expression $\Bigl\lfloor \frac{10^{2001}}{10^{29}-2} \Bigr\rfloor$

Spotting error in this solution: Solve for $x : [x] -2x= 4$

Differentiable analogue of greatest integer (a.k.a. floor) function

Difference of consecutive square floor functions.

discrete math (functions that include ceiling and floor

Can the sequence $\{\lfloor \alpha n \rfloor\}$ be divided into two parts with equal sums, for all $\alpha \in \mathbb{R}$?

Proving that $\int_a^b\frac1{\lfloor x\rfloor}\;\mathrm{d}x$ is irrational, given $b - a$ is irrational

Vietnam Mathematical Olympiad 2024 - First Question

Query Regarding Equation Solution and Floor Functions

Solve in real $x,\,\,\lfloor x^3\rfloor-3\lfloor x^2\rfloor+2\lfloor x\rfloor=0$

Why must $n-\lfloor\frac n2\rfloor+\lfloor\frac n3\rfloor-\dotsb$ grow like $n\ln2$?

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