Question

What is the asymptotic order of ${2n \choose 0}\sqrt{n}+ {2n \choose 1}\sqrt{n-1} +...+{2n \choose n}\sqrt{0}$?

score 356 · Answer 1 · 2018-05-14 18:26:11

356

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What is the asymptotic order of ${2n \choose 0}\sqrt{n}+ {2n \choose 1}\sqrt{n-1} +...+{2n \choose n}\sqrt{0}$?

Published on 14 May 2018 - 18:26

score 83 · Answer 2 · 2018-05-14 18:42:12

83

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Relation between summing over an infinite but countable set of elements, limits, integrals

Published on 14 May 2018 - 18:42

score 51 · Answer 3 · 2018-05-15 15:03:41

51

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Is it true that $\dfrac{n}{2\sqrt{n}-1}=\Theta(\sqrt{n})$?

Published on 15 May 2018 - 15:03

score 219 · Answer 4 · 2026-03-25 04:42:49

219

Views

How to find the divergence rate of a recursive sequence defined by $s_n = s_{n-1}(1 + c_n s_{n-1})$

Published on 25 Mar 2026 - 4:42

score 47 · Answer 5 · 2026-03-25 06:30:21

47

Views

Smoothness of $f^{-1}$ at $f(0)$ from asymptotics of $f:[0,\infty)\to \mathbb{R}$

Published on 25 Mar 2026 - 6:30

score 36 · Answer 6 · 2018-05-20 14:29:47

36

Views

Choosing c and $n_{0}$ for big-oh family definitions

Published on 20 May 2018 - 14:29

score 257 · Answer 7 · 2026-03-24 21:04:20

257

Views

Construct leading order approximation without given specific function

Published on 24 Mar 2026 - 21:04

score 645 · Answer 8 · 2026-03-25 01:18:41

645

Views

The asymptotics of the products over primes $\prod\limits_{2<p\le n}\left(1 - \frac1{p-1}\right)$

Published on 25 Mar 2026 - 1:18

score 120 · Answer 9 · 2018-05-21 20:14:18

120

Views

Continuity and convergence in probability, two sequences case

Published on 21 May 2018 - 20:14

score 245 · Answer 10 · 2018-05-22 08:57:33

245

Views

Multi-Gaussian Integrals with Heaviside for cosmic connectivity

Published on 22 May 2018 - 8:57

score 1.6k · Answer 11 · 2026-03-25 11:12:41

1.6k

Views

Log of the Moment Generating Function

Published on 25 Mar 2026 - 11:12

score 4.5k · Answer 12 · 2026-03-25 16:02:57

4.5k

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Leading terms in asymptotic expansion of modified bessel function of the first kind

Published on 25 Mar 2026 - 16:02

score 85 · Answer 13 · 2018-05-22 21:08:02

85

Views

Asymptotic Expansion (Taylor) when n goes to infinity of $ e^{-an}\sum_{k=n+1}^{\infty} \frac{(na)^k}{k!} $

Published on 22 May 2018 - 21:08

score 52 · Answer 14 · 2018-05-22 22:32:50

52

Views

Proving that $\ln^2(x) \le Cx$ for some $C >0$ ($x\ge1$)

Published on 22 May 2018 - 22:32

score 55 · Answer 15 · 2018-05-23 11:44:42

55

Views

Find the big-O of the sequence $a_{0} = a_{1} = 1, a_{n} = 2a_{n - 1} - 2a_{n - 2}$

Published on 23 May 2018 - 11:44

List Question

What is the asymptotic order of ${2n \choose 0}\sqrt{n}+ {2n \choose 1}\sqrt{n-1} +...+{2n \choose n}\sqrt{0}$?

Relation between summing over an infinite but countable set of elements, limits, integrals

Is it true that $\dfrac{n}{2\sqrt{n}-1}=\Theta(\sqrt{n})$?

How to find the divergence rate of a recursive sequence defined by $s_n = s_{n-1}(1 + c_n s_{n-1})$

Smoothness of $f^{-1}$ at $f(0)$ from asymptotics of $f:[0,\infty)\to \mathbb{R}$

Choosing c and $n_{0}$ for big-oh family definitions

Construct leading order approximation without given specific function

The asymptotics of the products over primes $\prod\limits_{2<p\le n}\left(1 - \frac1{p-1}\right)$

Continuity and convergence in probability, two sequences case

Multi-Gaussian Integrals with Heaviside for cosmic connectivity

Log of the Moment Generating Function

Leading terms in asymptotic expansion of modified bessel function of the first kind

Asymptotic Expansion (Taylor) when n goes to infinity of $ e^{-an}\sum_{k=n+1}^{\infty} \frac{(na)^k}{k!} $

Proving that $\ln^2(x) \le Cx$ for some $C >0$ ($x\ge1$)

Find the big-O of the sequence $a_{0} = a_{1} = 1, a_{n} = 2a_{n - 1} - 2a_{n - 2}$

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