Question

Missing steps: Show the sum of the first n positive integers is of order $n^2$

score 811 · Answer 1 · 2026-04-11 17:10:54

811

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Missing steps: Show the sum of the first n positive integers is of order $n^2$

Published on 11 Apr 2026 - 17:10

score 39 · Answer 2 · 2026-04-10 22:30:59

39

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what happens when expansion parameter is of the order of dynamical variable itself?

Published on 10 Apr 2026 - 22:30

score 114 · Answer 3 · 2026-04-15 18:35:13

114

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Estimate integral $\int\limits_0^{\infty}\operatorname{sech}\left(\varepsilon x\right)\cos\left(kx\right)\,dx,\,$ with $\,k,\varepsilon>0$

Published on 15 Apr 2026 - 18:35

score 310 · Answer 4 · 2026-04-13 20:32:10

310

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Why is $\binom{2n}{n} \asymp \Theta \big(\frac{2^{2n}}{\sqrt{n}}\big)$?

Published on 13 Apr 2026 - 20:32

score 384 · Answer 5 · 2026-04-15 03:57:21

384

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Arithmetic progression of squarefree integers?

Published on 15 Apr 2026 - 3:57

score 419 · Answer 6 · 2026-04-15 05:55:49

419

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How to show that $O(n^\frac{3}{4} \log n) = O(n)$?

Published on 15 Apr 2026 - 5:55

score 147 · Answer 7 · 2026-04-08 02:27:22

147

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Asymptotic error expansion of global error for single step methods

Published on 08 Apr 2026 - 2:27

score 93 · Answer 8 · 2026-04-14 14:20:33

93

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Each number in $S\subseteq \{1,\ldots,2n\}$ does not divide another one, with $|S|= n$. In how many ways?

Published on 14 Apr 2026 - 14:20

score 4.5k · Answer 9 · 2026-04-12 22:21:15

4.5k

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Product property of Big O

Published on 12 Apr 2026 - 22:21

score 1.1k · Answer 10 · 2026-04-14 23:00:46

1.1k

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Large pairwise coprime sets

Published on 14 Apr 2026 - 23:00

score 70 · Answer 11 · 2026-04-16 16:29:00

70

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Simplifying $f(x) = \left(x^{3} + 2x^{2} + O(x)\right)\cdot\left(1 + \frac{1}{x} + O\left(\frac{1}{x^{2}}\right)\right) $

Published on 16 Apr 2026 - 16:29

score 32 · Answer 12 · 2026-04-14 01:21:30

32

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asymptotic of an interesting recurrence realtion (more general case)

Published on 14 Apr 2026 - 1:21

score 93 · Answer 13 · 2026-04-15 14:33:45

93

Views

What is the big Oh notation for the following series.

Published on 15 Apr 2026 - 14:33

score 2.3k · Answer 14 · 2026-04-14 11:38:34

2.3k

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$O( n^3)$ vs $O(n^2 \ log n)$

Published on 14 Apr 2026 - 11:38

score 413 · Answer 15 · 2026-04-30 02:58:30

413

Views

Name for kind of big O notation with leading coefficient

Published on 30 Apr 2026 - 2:58

List Question

Missing steps: Show the sum of the first n positive integers is of order $n^2$

what happens when expansion parameter is of the order of dynamical variable itself?

Estimate integral $\int\limits_0^{\infty}\operatorname{sech}\left(\varepsilon x\right)\cos\left(kx\right)\,dx,\,$ with $\,k,\varepsilon>0$

Why is $\binom{2n}{n} \asymp \Theta \big(\frac{2^{2n}}{\sqrt{n}}\big)$?

Arithmetic progression of squarefree integers?

How to show that $O(n^\frac{3}{4} \log n) = O(n)$?

Asymptotic error expansion of global error for single step methods

Each number in $S\subseteq \{1,\ldots,2n\}$ does not divide another one, with $|S|= n$. In how many ways?

Product property of Big O

Large pairwise coprime sets

Simplifying $f(x) = \left(x^{3} + 2x^{2} + O(x)\right)\cdot\left(1 + \frac{1}{x} + O\left(\frac{1}{x^{2}}\right)\right) $

asymptotic of an interesting recurrence realtion (more general case)

What is the big Oh notation for the following series.

$O( n^3)$ vs $O(n^2 \ log n)$

Name for kind of big O notation with leading coefficient

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