Question

Prove $[\sqrt{x}+\sqrt{x+1}]=[\sqrt{4x+2}], x \in \Bbb N$

score 273 · Answer 1 · 2015-11-23 13:28:25

273

Views

Prove $[\sqrt{x}+\sqrt{x+1}]=[\sqrt{4x+2}], x \in \Bbb N$

Published on 23 Nov 2015 - 13:28

score 486 · Answer 2 · 2015-11-23 14:25:39

486

Views

Calculate limit with floor function

Published on 23 Nov 2015 - 14:25

score 4.5k · Answer 3 · 2015-11-24 09:55:24

4.5k

Views

What technique should I apply to find the derivative of a ceiling or floor function e.g d/dx(x⌈x⌉) and d/dx(x⌊x⌋)?

Published on 24 Nov 2015 - 9:55

score 1.4k · Answer 4 · 2026-03-30 05:28:52

1.4k

Views

Are these trigonometric expressions for the ceiling and floor functions correct?

Published on 30 Mar 2026 - 5:28

score 147 · Answer 5 · 2015-11-26 14:02:39

147

Views

$\lfloor\frac{1}{x}\rfloor\cdot x^2$ continuous at $0$

Published on 26 Nov 2015 - 14:02

score 197 · Answer 6 · 2015-11-28 21:09:02

197

Views

Floor and Ceiling functions

Published on 28 Nov 2015 - 21:09

score 284 · Answer 7 · 2015-11-29 20:31:06

284

Views

What is $\lfloor(\sqrt 3 +1)^5\rfloor$? (without a calculator)

Published on 29 Nov 2015 - 20:31

score 39 · Answer 8 · 2015-11-30 00:02:08

39

Views

Difference between the integral of floor and the triangular series

Published on 30 Nov 2015 - 0:02

score 2.5k · Answer 9 · 2015-12-03 10:55:10

2.5k

Views

Summation of Greatest Integer $ \sum_{k=1}^{n} \left \lfloor{\sqrt{k}}\right \rfloor $

Published on 03 Dec 2015 - 10:55

score 64 · Answer 10 · 2015-12-06 07:06:45

64

Views

Why does the floor function $x \mapsto \lfloor x \rfloor$ have expansion $x + O(1)$?

Published on 06 Dec 2015 - 7:06

score 56 · Answer 11 · 2015-12-06 07:39:09

56

Views

If we have a sequence of 1's, why is the partial sum of it equal to a floor function?

Published on 06 Dec 2015 - 7:39

score 190 · Answer 12 · 2015-12-08 16:08:58

190

Views

Assistance in finding $\lim_{n\to\infty} \frac{n-\lfloor \sqrt n \rfloor^2}{n}$

Published on 08 Dec 2015 - 16:08

score 106 · Answer 13 · 2015-12-08 21:03:27

106

Views

Waring's Problem and the floor function - solving a recurrence relation by hand

Published on 08 Dec 2015 - 21:03

score 288 · Answer 14 · 2015-12-09 09:49:39

288

Views

Derivatives and discontinuity with ceiling function

Published on 09 Dec 2015 - 9:49

score 197 · Answer 15 · 2015-12-19 17:44:25

197

Views

I would like to calculate $\lim_ {n \to \infty} {\frac{n+\lfloor \sqrt{n} \rfloor^2}{n-\lfloor \sqrt{n} \rfloor}}$

Published on 19 Dec 2015 - 17:44

List Question

Prove $[\sqrt{x}+\sqrt{x+1}]=[\sqrt{4x+2}], x \in \Bbb N$

Calculate limit with floor function

What technique should I apply to find the derivative of a ceiling or floor function e.g d/dx(x⌈x⌉) and d/dx(x⌊x⌋)?

Are these trigonometric expressions for the ceiling and floor functions correct?

$\lfloor\frac{1}{x}\rfloor\cdot x^2$ continuous at $0$

Floor and Ceiling functions

What is $\lfloor(\sqrt 3 +1)^5\rfloor$? (without a calculator)

Difference between the integral of floor and the triangular series

Summation of Greatest Integer $ \sum_{k=1}^{n} \left \lfloor{\sqrt{k}}\right \rfloor $

Why does the floor function $x \mapsto \lfloor x \rfloor$ have expansion $x + O(1)$?

If we have a sequence of 1's, why is the partial sum of it equal to a floor function?

Assistance in finding $\lim_{n\to\infty} \frac{n-\lfloor \sqrt n \rfloor^2}{n}$

Waring's Problem and the floor function - solving a recurrence relation by hand

Derivatives and discontinuity with ceiling function

I would like to calculate $\lim_ {n \to \infty} {\frac{n+\lfloor \sqrt{n} \rfloor^2}{n-\lfloor \sqrt{n} \rfloor}}$

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