Question

Proving $\lim _{n\to\infty}\frac{1}{ a_n} \neq \alpha$ given $\lim _{n\to\infty}a_n = 0$ and...

score 94 · Answer 1 · 2026-03-25 23:11:08

94

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Proving $\lim _{n\to\infty}\frac{1}{ a_n} \neq \alpha$ given $\lim _{n\to\infty}a_n = 0$ and...

Published on 25 Mar 2026 - 23:11

score 166 · Answer 2 · 2026-03-25 23:16:35

166

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Calculating $\lim\limits_{n\to\infty}\frac{1+2+3+...+n-1}{n^2}$

Published on 25 Mar 2026 - 23:16

score 204 · Answer 3 · 2026-03-25 23:13:08

204

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Calculating $\lim_{n\to\infty}\left(\frac{\sin(2\sqrt 1)}{n\sqrt 1\cos\sqrt 1} +\cdots+\frac{\sin(2\sqrt n)}{n\sqrt n\cos\sqrt n}\right)$

Published on 25 Mar 2026 - 23:13

score 67 · Answer 4 · 2026-03-25 23:11:09

67

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Determine that if $a_n \longrightarrow L$ then $\sqrt[n]{a_1\cdot...a_n}\longrightarrow L$

Published on 25 Mar 2026 - 23:11

score 89 · Answer 5 · 2026-03-25 23:11:15

89

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Proving $\displaystyle{\lim _{n\to\infty}}\sqrt[n]{n} = 1$ given that $\inf \{\sqrt[n]{n}|n\in \mathbb{N}\} = 1$

Published on 25 Mar 2026 - 23:11

score 164 · Answer 6 · 2026-03-25 23:08:04

164

Views

Can infinitesimals be limits to sequences?

Published on 25 Mar 2026 - 23:08

score 67 · Answer 7 · 2026-03-25 23:08:07

67

Views

Difference between $\lim_{x \to 0} \text{ and } x=0$

Published on 25 Mar 2026 - 23:08

score 67 · Answer 8 · 2026-05-10 14:32:35

67

Views

Number of equal pairs from a set of size n in range 1-nlog

Published on 10 May 2026 - 14:32

score 215 · Answer 9 · 2026-04-29 03:37:47

215

Views

Smooth real line and Dedekind cuts

Published on 29 Apr 2026 - 3:37

score 61 · Answer 10 · 2026-05-10 20:02:52

61

Views

What hyperreal functions satisfy this condition involving positive infinitesimals?

Published on 10 May 2026 - 20:02

score 104 · Answer 11 · 2026-05-10 20:03:59

104

Views

Using hyperreals to express the interval of uniform convergence of $x^n$ in a closed form

Published on 10 May 2026 - 20:03

score 159 · Answer 12 · 2026-03-25 23:08:35

159

Views

Thompson's Calculus Made Easy: Confusion About Differentials When Differentiating $y=x^2$

Published on 25 Mar 2026 - 23:08

score 36 · Answer 13 · 2026-05-10 16:58:45

36

Views

Filtration infinitesimal glance into the future

Published on 10 May 2026 - 16:58

score 42 · Answer 14 · 2026-05-10 13:49:08

42

Views

Uniformly Bounded Functions of Hyperreals

Published on 10 May 2026 - 13:49

score 49 · Answer 15 · 2026-03-25 23:09:32

49

Views

Help phrasing (geometric?) probability distribution-like problem without rigorously invoking limit

Published on 25 Mar 2026 - 23:09

List Question

Proving $\lim _{n\to\infty}\frac{1}{ a_n} \neq \alpha$ given $\lim _{n\to\infty}a_n = 0$ and...

Calculating $\lim\limits_{n\to\infty}\frac{1+2+3+...+n-1}{n^2}$

Calculating $\lim_{n\to\infty}\left(\frac{\sin(2\sqrt 1)}{n\sqrt 1\cos\sqrt 1} +\cdots+\frac{\sin(2\sqrt n)}{n\sqrt n\cos\sqrt n}\right)$

Determine that if $a_n \longrightarrow L$ then $\sqrt[n]{a_1\cdot...a_n}\longrightarrow L$

Proving $\displaystyle{\lim _{n\to\infty}}\sqrt[n]{n} = 1$ given that $\inf \{\sqrt[n]{n}|n\in \mathbb{N}\} = 1$

Can infinitesimals be limits to sequences?

Difference between $\lim_{x \to 0} \text{ and } x=0$

Number of equal pairs from a set of size n in range 1-nlog

Smooth real line and Dedekind cuts

What hyperreal functions satisfy this condition involving positive infinitesimals?

Using hyperreals to express the interval of uniform convergence of $x^n$ in a closed form

Thompson's Calculus Made Easy: Confusion About Differentials When Differentiating $y=x^2$

Filtration infinitesimal glance into the future

Uniformly Bounded Functions of Hyperreals

Help phrasing (geometric?) probability distribution-like problem without rigorously invoking limit

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