Question

$(\sum_{k\in[\sqrt{n},n-\sqrt{n}]}1)$ vanishes in $\frac{1}{n}(\sum_{k\in[\sqrt{n},n-\sqrt{n}]}1)(M+|\alpha|)$

score 41 · Answer 1 · 2026-04-15 13:40:38

41

Views

$(\sum_{k\in[\sqrt{n},n-\sqrt{n}]}1)$ vanishes in $\frac{1}{n}(\sum_{k\in[\sqrt{n},n-\sqrt{n}]}1)(M+|\alpha|)$

Published on 15 Apr 2026 - 13:40

score 120 · Answer 2 · 2026-04-14 21:35:39

120

Views

If $x\in\mathbb{R}\setminus\mathbb{Z}$ and if $x_n \to x $ then $\lfloor x_n \rfloor \to \lfloor x \rfloor$

Published on 14 Apr 2026 - 21:35

score 244 · Answer 3 · 2026-04-15 20:33:05

244

Views

What is $\lim\limits_{n \rightarrow \infty} \frac{\sqrt{n+1} + 3}{\sqrt{n+2} - 4}$?

Published on 15 Apr 2026 - 20:33

score 210 · Answer 4 · 2026-04-14 11:27:02

210

Views

How can I find the limit of a sequence containing $\sin n!$?

Published on 14 Apr 2026 - 11:27

score 122 · Answer 5 · 2026-04-17 07:27:45

122

Views

Let $a_n = n^{1/n}$ and $b_n = {a_{n+1}}/{a_n}$, prove that $\{b_n\}_{n=5}^{\infty}$ is increasing.

Published on 17 Apr 2026 - 7:27

score 385 · Answer 6 · 2026-04-16 14:22:54

385

Views

A sequence of full rank matrices $A_i \in \mathbb{R}^{m\times n}$ such that $A_i \rightarrow A$ in $\|\cdot\|_2$

Published on 16 Apr 2026 - 14:22

score 57 · Answer 7 · 2026-04-09 15:22:29

57

Views

Interval of convergence, pointwise and absolute

Published on 09 Apr 2026 - 15:22

score 65 · Answer 8 · 2026-04-16 01:10:56

65

Views

Find a sequence converging to $\{1/k\}^{\infty}_{k=1}$ in $l^2$

Published on 16 Apr 2026 - 1:10

score 1k · Answer 9 · 2026-04-16 01:30:57

1k

Views

Closed form for $t_n = 6t_{n-1}-9t_{n-2}$ where $t_0 = 5$ and $t_1 = 9$

Published on 16 Apr 2026 - 1:30

score 42 · Answer 10 · 2026-04-11 06:49:50

42

Views

How are convergence tests proved?

Published on 11 Apr 2026 - 6:49

score 75 · Answer 11 · 2026-04-15 17:16:10

75

Views

Is $f(x)=x^2+\frac{x^2}{1+x^2}+\frac{x^2}{(1+x^2)^2}+\dots,x \in \Bbb{R}$ continuos?

Published on 15 Apr 2026 - 17:16

score 174 · Answer 12 · 2026-04-29 19:15:16

174

Views

How to prove a probability measure is relatively compact？

Published on 29 Apr 2026 - 19:15

score 113 · Answer 13 · 2026-04-15 05:43:58

113

Views

How do you calculate this infinite series $\sum_{n=0}^\infty \frac{\binom{2n+1}{n-p}}{(4^n)(2n+1)(1.25)^{2n+1}}$?

Published on 15 Apr 2026 - 5:43

score 306 · Answer 14 · 2026-04-11 16:05:52

306

Views

What is the closed form for $ \sum\limits_{n=0}^{\infty}\frac{1}{(n!)^2}$?

Published on 11 Apr 2026 - 16:05

score 124 · Answer 15 · 2026-04-13 15:55:09

124

Views

Bartle Analysis (Sequence) Theorem 3.2.4 Proof question

Published on 13 Apr 2026 - 15:55

List Question

$(\sum_{k\in[\sqrt{n},n-\sqrt{n}]}1)$ vanishes in $\frac{1}{n}(\sum_{k\in[\sqrt{n},n-\sqrt{n}]}1)(M+|\alpha|)$

If $x\in\mathbb{R}\setminus\mathbb{Z}$ and if $x_n \to x $ then $\lfloor x_n \rfloor \to \lfloor x \rfloor$

What is $\lim\limits_{n \rightarrow \infty} \frac{\sqrt{n+1} + 3}{\sqrt{n+2} - 4}$?

How can I find the limit of a sequence containing $\sin n!$?

Let $a_n = n^{1/n}$ and $b_n = {a_{n+1}}/{a_n}$, prove that $\{b_n\}_{n=5}^{\infty}$ is increasing.

A sequence of full rank matrices $A_i \in \mathbb{R}^{m\times n}$ such that $A_i \rightarrow A$ in $\|\cdot\|_2$

Interval of convergence, pointwise and absolute

Find a sequence converging to $\{1/k\}^{\infty}_{k=1}$ in $l^2$

Closed form for $t_n = 6t_{n-1}-9t_{n-2}$ where $t_0 = 5$ and $t_1 = 9$

How are convergence tests proved?

Is $f(x)=x^2+\frac{x^2}{1+x^2}+\frac{x^2}{(1+x^2)^2}+\dots,x \in \Bbb{R}$ continuos?

How to prove a probability measure is relatively compact？

How do you calculate this infinite series $\sum_{n=0}^\infty \frac{\binom{2n+1}{n-p}}{(4^n)(2n+1)(1.25)^{2n+1}}$?

What is the closed form for $ \sum\limits_{n=0}^{\infty}\frac{1}{(n!)^2}$?

Bartle Analysis (Sequence) Theorem 3.2.4 Proof question

Trending Questions

Popular # Hahtags

Popular Questions