Question

Continuity of $f(x) = \left\lfloor {x^2} \right\rfloor - {\left\lfloor {x} \right\rfloor}^2$

score 136 · Answer 1 · 2022-08-27 06:16:02

136

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Continuity of $f(x) = \left\lfloor {x^2} \right\rfloor - {\left\lfloor {x} \right\rfloor}^2$

Published on 27 Aug 2022 - 6:16

score 97 · Answer 2 · 2026-03-25 15:42:35

97

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Is there a way to compute an asymptotic formula of $\sum_{n\leq x}\lceil 2\sqrt{n} \rceil$?

Published on 25 Mar 2026 - 15:42

score 88 · Answer 3 · 2022-08-30 15:41:56

88

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Is it possible to calculate how many digit number I have to write if I write $n^2$ sequence from 1 to $1000^2$ without using calculator?

Published on 30 Aug 2022 - 15:41

score 120 · Answer 4 · 2022-08-31 01:21:11

120

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prove it $\displaystyle\sum _{ i=1 }^{ \infty }{\biggl\lfloor \frac{n}{2^{i}}+\frac{1}{2}\biggr\rfloor}=n$

Published on 31 Aug 2022 - 1:21

score 48 · Answer 5 · 2022-08-31 13:33:36

48

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I just want to know if this is right method of doing this question.

Published on 31 Aug 2022 - 13:33

score 71 · Answer 6 · 2022-09-02 22:16:13

71

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How to proceed with a definite integral of this form?

Published on 02 Sep 2022 - 22:16

score 52 · Answer 7 · 2026-03-31 22:28:03

52

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The permutation that minimizes the sum of floor(a_i / i)

Published on 31 Mar 2026 - 22:28

score 128 · Answer 8 · 2022-09-05 11:30:40

128

Views

Proving $\sum_{1}^{n} \left\lceil\log_{2}\frac{2n}{2i-1}\right\rceil=2n -1 $

Published on 05 Sep 2022 - 11:30

score 211 · Answer 9 · 2022-09-05 23:28:18

211

Views

Can we show algebraically that this is true?

Published on 05 Sep 2022 - 23:28

score 69 · Answer 10 · 2026-04-01 09:48:50

69

Views

Prove ceil inequality with powers of 2 holds for all real numbers from $(1,2)$

Published on 01 Apr 2026 - 9:48

score 75 · Answer 11 · 2022-09-09 04:05:18

75

Views

How to bound $\int_{1}^x \frac{\sin([t])}t\,\mathrm dt$?

Published on 09 Sep 2022 - 4:05

score 56 · Answer 12 · 2026-03-29 06:46:49

56

Views

How to show that the expression can be made arbitrarily close to 0?

Published on 29 Mar 2026 - 6:46

score 207 · Answer 13 · 2022-09-12 18:02:52

207

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Is this proof of $\left\lfloor \frac{n}{m} \right\rfloor = \left\lceil \frac{n-m+1}{m} \right\rceil$ correct?

Published on 12 Sep 2022 - 18:02

score 104 · Answer 14 · 2026-03-26 01:12:45

104

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Is there a way to calculate the exact birthdate of a person based on a series of dates and ages?

Published on 26 Mar 2026 - 1:12

score 114 · Answer 15 · 2022-09-15 19:57:27

114

Views

$U_{n} + \lfloor \sqrt{U_{n}} \rfloor = k^{2}$

Published on 15 Sep 2022 - 19:57

List Question

Continuity of $f(x) = \left\lfloor {x^2} \right\rfloor - {\left\lfloor {x} \right\rfloor}^2$

Is there a way to compute an asymptotic formula of $\sum_{n\leq x}\lceil 2\sqrt{n} \rceil$?

Is it possible to calculate how many digit number I have to write if I write $n^2$ sequence from 1 to $1000^2$ without using calculator?

prove it $\displaystyle\sum _{ i=1 }^{ \infty }{\biggl\lfloor \frac{n}{2^{i}}+\frac{1}{2}\biggr\rfloor}=n$

I just want to know if this is right method of doing this question.

How to proceed with a definite integral of this form?

The permutation that minimizes the sum of floor(a_i / i)

Proving $\sum_{1}^{n} \left\lceil\log_{2}\frac{2n}{2i-1}\right\rceil=2n -1 $

Can we show algebraically that this is true?

Prove ceil inequality with powers of 2 holds for all real numbers from $(1,2)$

How to bound $\int_{1}^x \frac{\sin([t])}t\,\mathrm dt$?

How to show that the expression can be made arbitrarily close to 0?

Is this proof of $\left\lfloor \frac{n}{m} \right\rfloor = \left\lceil \frac{n-m+1}{m} \right\rceil$ correct?

Is there a way to calculate the exact birthdate of a person based on a series of dates and ages?

$U_{n} + \lfloor \sqrt{U_{n}} \rfloor = k^{2}$

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