Question

Show that $(-1)^{n}\left(\sqrt{n+1}-\sqrt{n} \right)=\tfrac{(-1)^{n}}{2\sqrt{n}}+\mathcal{O}\left(\tfrac{1}{n^{3/2}} \right)$

score 105 · Answer 1 · 2026-04-12 02:01:10

105

Views

Show that $(-1)^{n}\left(\sqrt{n+1}-\sqrt{n} \right)=\tfrac{(-1)^{n}}{2\sqrt{n}}+\mathcal{O}\left(\tfrac{1}{n^{3/2}} \right)$

Published on 12 Apr 2026 - 2:01

score 37 · Answer 2 · 2016-07-14 15:35:10

37

Views

$X-x_0=O_p(n^{-1/2})$ implies $g(X)-g(x_0)=O_p(n^{-1/2})$

Published on 14 Jul 2016 - 15:35

score 70 · Answer 3 · 2026-04-12 02:01:10

70

Views

Show that $(-1)^{n}\sqrt[n]{n}\sin(\frac{1}{n})=\tfrac{(-1)^{n}}{n}+\mathcal{O}\left(\tfrac{\ln(n)}{n^{2}} \right)$

Published on 12 Apr 2026 - 2:01

score 24 · Answer 4 · 2026-04-12 02:01:09

Show that $\tfrac{(-1)^{n}}{\cos(n)+n^{\tfrac{3}{4}}}=\tfrac{(-1)^{n}}{n^{\tfrac{3}{4}}}+\mathcal{O}\left( \tfrac{1}{n^{\tfrac{3}{2}}}\right) $

score 73 · Answer 5 · 2026-04-12 02:01:09

Show : $(-1)^{n}n^{-\tan\left(\tfrac{\pi}{4}+\tfrac{1}{n} \right)}=\tfrac{(-1)^{n}}{n}+\mathcal{O}\left(\tfrac{\ln(n)}{n^{2}} \right)$

score 294 · Answer 6 · 2016-07-15 19:08:57

294

Views

Growth of $\pi(2x) - 2\pi(x)$

Published on 15 Jul 2016 - 19:08

score 38 · Answer 7 · 2026-03-30 16:30:04

38

Views

When is $\frac{2 n f(n)}{n !}$ in the order of some fixed power of $n$?

Published on 30 Mar 2026 - 16:30

score 423 · Answer 8 · 2016-07-17 19:18:40

423

Views

What is the value of $I=\lim_{n \to \infty} \int_0^1 {{1 + nx^2}\over{(1 + x^2)^n}} \log(2 + \cos(x/n))\,dx.$?

Published on 17 Jul 2016 - 19:18

score 167 · Answer 9 · 2026-03-25 22:11:21

167

Views

Asymptotic expansion of elliptic integral

Published on 25 Mar 2026 - 22:11

score 91 · Answer 10 · 2026-04-12 17:02:20

91

Views

Can you provide us an asymptotic for this series involving Mertens functions?

Published on 12 Apr 2026 - 17:02

score 567 · Answer 11 · 2026-04-10 16:54:27

567

Views

How to concretely interpret big O bounds on error for forward euler?

Published on 10 Apr 2026 - 16:54

score 4.3k · Answer 12 · 2026-04-11 15:00:38

4.3k

Views

Can two function be Big-O of each other?

Published on 11 Apr 2026 - 15:00

score 72 · Answer 13 · 2026-04-12 03:53:27

72

Views

nature of the series $\sum (-1)^{n}n^{-\tan\left(\tfrac{\pi}{4}+\tfrac{1}{n} \right)}$

Published on 12 Apr 2026 - 3:53

score 141 · Answer 14 · 2026-04-10 22:31:56

141

Views

What is difference between $O(|V|+|E|)$ and $O(|V+E|)$?

Published on 10 Apr 2026 - 22:31

score 47 · Answer 15 · 2026-03-26 08:00:28

47

Views

Asymptotic solution of the equation $\gamma_{i+2} + 4\gamma_{i+1} + \gamma_{i} = \frac{Kh^2}{12}$

Published on 26 Mar 2026 - 8:00

List Question

Show that $(-1)^{n}\left(\sqrt{n+1}-\sqrt{n} \right)=\tfrac{(-1)^{n}}{2\sqrt{n}}+\mathcal{O}\left(\tfrac{1}{n^{3/2}} \right)$

$X-x_0=O_p(n^{-1/2})$ implies $g(X)-g(x_0)=O_p(n^{-1/2})$

Show that $(-1)^{n}\sqrt[n]{n}\sin(\frac{1}{n})=\tfrac{(-1)^{n}}{n}+\mathcal{O}\left(\tfrac{\ln(n)}{n^{2}} \right)$

Show that $\tfrac{(-1)^{n}}{\cos(n)+n^{\tfrac{3}{4}}}=\tfrac{(-1)^{n}}{n^{\tfrac{3}{4}}}+\mathcal{O}\left( \tfrac{1}{n^{\tfrac{3}{2}}}\right) $

Show : $(-1)^{n}n^{-\tan\left(\tfrac{\pi}{4}+\tfrac{1}{n} \right)}=\tfrac{(-1)^{n}}{n}+\mathcal{O}\left(\tfrac{\ln(n)}{n^{2}} \right)$

Growth of $\pi(2x) - 2\pi(x)$

When is $\frac{2 n f(n)}{n !}$ in the order of some fixed power of $n$?

What is the value of $I=\lim_{n \to \infty} \int_0^1 {{1 + nx^2}\over{(1 + x^2)^n}} \log(2 + \cos(x/n))\,dx.$?

Asymptotic expansion of elliptic integral

Can you provide us an asymptotic for this series involving Mertens functions?

How to concretely interpret big O bounds on error for forward euler?

Can two function be Big-O of each other?

nature of the series $\sum (-1)^{n}n^{-\tan\left(\tfrac{\pi}{4}+\tfrac{1}{n} \right)}$

What is difference between $O(|V|+|E|)$ and $O(|V+E|)$?

Asymptotic solution of the equation $\gamma_{i+2} + 4\gamma_{i+1} + \gamma_{i} = \frac{Kh^2}{12}$

Trending Questions

Popular # Hahtags

Popular Questions