Question

for [ f(n) = Sum(1:n) , g(n) = n^2 ] , why does ( f isIn O(g) AND g isIn O(f) ) hold?

score 28 · Answer 1 · 2026-04-16 04:47:31

28

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for [ f(n) = Sum(1:n) , g(n) = n^2 ] , why does ( f isIn O(g) AND g isIn O(f) ) hold?

Published on 16 Apr 2026 - 4:47

score 129 · Answer 2 · 2026-04-14 07:51:30

129

Views

Two closest sums of pairs of reciprocals

Published on 14 Apr 2026 - 7:51

score 438 · Answer 3 · 2026-04-09 00:55:50

438

Views

Asymptotic expansion of double integral

Published on 09 Apr 2026 - 0:55

score 41 · Answer 4 · 2026-04-13 22:54:40

41

Views

How to derive bounds for the $n$-th term of a subsequence of $\mathbb {N} $, knowing two functions "squeezing" the number of the terms below $x$?

Published on 13 Apr 2026 - 22:54

score 130 · Answer 5 · 2026-04-15 23:34:29

130

Views

Find this limits $\lim_{n\to\infty}n^2\bigl(n(H_{2n}-H_{n}-\ln{2})+\frac{1}{4}\bigr)$

Published on 15 Apr 2026 - 23:34

score 169 · Answer 6 · 2026-04-16 07:08:12

169

Views

How do i prove this inequality

Published on 16 Apr 2026 - 7:08

score 76 · Answer 7 · 2026-04-15 10:55:43

76

Views

Asymptotic behaviour of $\sum_{k=0}^\infty \frac{n^k}{(k!)^\nu}$

Published on 15 Apr 2026 - 10:55

score 563 · Answer 8 · 2026-04-25 15:10:41

563

Views

Asymptotic behaviour of a recurrence relation - How to solve

Published on 25 Apr 2026 - 15:10

score 251 · Answer 9 · 2026-04-25 16:43:45

251

Views

Find a big-O estimate for $f(n)=2f(\sqrt{n})+1$

Published on 25 Apr 2026 - 16:43

score 665 · Answer 10 · 2026-04-10 07:13:29

665

Views

Finding big O of a function

Published on 10 Apr 2026 - 7:13

score 66 · Answer 11 · 2026-04-15 13:34:45

66

Views

Can we deduce that $⌊r^{n}α⌋≃r^{n}α$ when $r→∞$?

Published on 15 Apr 2026 - 13:34

score 53 · Answer 12 · 2026-04-16 05:27:24

53

Views

If I colour $n$ vertices independently, randomly with $n^{(1-x)}$ colours, why is the size of the colour classes $(1+o(1))n^x$?

Published on 16 Apr 2026 - 5:27

score 81 · Answer 13 · 2026-04-16 18:31:40

81

Views

Is $f(n)=O(g(n))$ or $f(n)=\Omega(g(n))$ when $f(n) = (\log n)^{\log n}$ and $g(n) = n/\log n$?

Published on 16 Apr 2026 - 18:31

score 150 · Answer 14 · 2026-04-17 02:12:34

150

Views

How can I show this sequence $u_n$ is divergent: $u_n=\exp( n\log n-(n+\epsilon)\log(n+\epsilon))$

Published on 17 Apr 2026 - 2:12

score 92 · Answer 15 · 2026-04-16 15:35:05

92

Views

How do I find the equivalence of the expression $e^{n\log(n)-(n+e)\log(n + e)}$?

Published on 16 Apr 2026 - 15:35

List Question

for [ f(n) = Sum(1:n) , g(n) = n^2 ] , why does ( f isIn O(g) AND g isIn O(f) ) hold?

Two closest sums of pairs of reciprocals

Asymptotic expansion of double integral

How to derive bounds for the $n$-th term of a subsequence of $\mathbb {N} $, knowing two functions "squeezing" the number of the terms below $x$?

Find this limits $\lim_{n\to\infty}n^2\bigl(n(H_{2n}-H_{n}-\ln{2})+\frac{1}{4}\bigr)$

How do i prove this inequality

Asymptotic behaviour of $\sum_{k=0}^\infty \frac{n^k}{(k!)^\nu}$

Asymptotic behaviour of a recurrence relation - How to solve

Find a big-O estimate for $f(n)=2f(\sqrt{n})+1$

Finding big O of a function

Can we deduce that $⌊r^{n}α⌋≃r^{n}α$ when $r→∞$?

If I colour $n$ vertices independently, randomly with $n^{(1-x)}$ colours, why is the size of the colour classes $(1+o(1))n^x$?

Is $f(n)=O(g(n))$ or $f(n)=\Omega(g(n))$ when $f(n) = (\log n)^{\log n}$ and $g(n) = n/\log n$?

How can I show this sequence $u_n$ is divergent: $u_n=\exp( n\log n-(n+\epsilon)\log(n+\epsilon))$

How do I find the equivalence of the expression $e^{n\log(n)-(n+e)\log(n + e)}$?

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