Question

$\sum_\limits{n=1}^{\infty}\frac{n}{x^n}$ ratio or root test? different results?

score 81 · Answer 1 · 2026-04-18 13:35:54

81

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$\sum_\limits{n=1}^{\infty}\frac{n}{x^n}$ ratio or root test? different results?

Published on 18 Apr 2026 - 13:35

score 90 · Answer 2 · 2026-05-10 14:50:24

90

Views

Is $\mathcal{E}' \ni u \mapsto \hat{u} \in C^\infty$ sequentially continuous?

Published on 10 May 2026 - 14:50

score 86 · Answer 3 · 2026-05-05 01:13:41

86

Views

How to prove the following function has only one root in interval [0,1]

Published on 05 May 2026 - 1:13

score 68 · Answer 4 · 2026-04-16 00:40:12

68

Views

Prove that $\lim_{y \to x-}f(y) = a$ if for every sequence $(x_n)_n$ in $\mathbb{R}$ that increases towards x, the sequence $f(x_n)$ converges to $a$

Published on 16 Apr 2026 - 0:40

score 43 · Answer 5 · 2026-04-14 23:21:25

43

Views

Class $C$ functions

Published on 14 Apr 2026 - 23:21

score 581 · Answer 6 · 2026-04-12 12:24:51

581

Views

Product expansion of cosine

Published on 12 Apr 2026 - 12:24

score 56 · Answer 7 · 2026-05-14 17:13:38

56

Views

Prove that $f^{*}(y) =\frac{\|y\|^q}{q}$; $\frac{1}{p}+\frac{1}{q}=1$?

Published on 14 May 2026 - 17:13

score 134 · Answer 8 · 2026-04-11 11:13:36

134

Views

$\liminf$ and $\limsup$ of real sequences and their Cesaro averages

Published on 11 Apr 2026 - 11:13

score 116 · Answer 9 · 2026-04-11 19:45:40

116

Views

Studying convergence of $\sum\limits_{k=1}^{\infty}\frac{k!\exp(k)}{(k+1)^k}$

Published on 11 Apr 2026 - 19:45

score 1.4k · Answer 10 · 2026-04-16 16:32:31

1.4k

Views

Steffensen's method. Consider the iteration formula $x_{n+1}=x_n-f(x_n)/g(x_n)$ where $g(x)=[f(x+f(x))-f(x)]/f(x)$. Show that this quadratically

Published on 16 Apr 2026 - 16:32

score 1.7k · Answer 11 · 2026-04-13 20:14:55

1.7k

Views

Is there a sequence of unbounded closed intervals such that its intersection is empty?

Published on 13 Apr 2026 - 20:14

score 95 · Answer 12 · 2026-04-14 02:50:18

95

Views

Set $\{x | f(x) = \infty\}$ is of measure 0.

Published on 14 Apr 2026 - 2:50

score 47 · Answer 13 · 2026-04-12 00:30:47

47

Views

Under what circumstances is this function continuous?

Published on 12 Apr 2026 - 0:30

score 357 · Answer 14 · 2026-04-16 08:25:30

357

Views

If $f(x) = { x^2 \sin \frac 1 x \text{ for } 0 < x \leq 1}$ and $f(0)=0$, prove $f$ is rectifiable.

Published on 16 Apr 2026 - 8:25

score 473 · Answer 15 · 2026-04-14 00:32:40

473

Views

Prove that $\sum\limits_{k=1}^{n}\frac{|z_{k}|^2}{|z_{k+1}-z_{k}|^2}\ge 1$ for complex numbers $z_k$'s

Published on 14 Apr 2026 - 0:32

List Question

$\sum_\limits{n=1}^{\infty}\frac{n}{x^n}$ ratio or root test? different results?

Is $\mathcal{E}' \ni u \mapsto \hat{u} \in C^\infty$ sequentially continuous?

How to prove the following function has only one root in interval [0,1]

Prove that $\lim_{y \to x-}f(y) = a$ if for every sequence $(x_n)_n$ in $\mathbb{R}$ that increases towards x, the sequence $f(x_n)$ converges to $a$

Class $C$ functions

Product expansion of cosine

Prove that $f^{*}(y) =\frac{\|y\|^q}{q}$; $\frac{1}{p}+\frac{1}{q}=1$?

$\liminf$ and $\limsup$ of real sequences and their Cesaro averages

Studying convergence of $\sum\limits_{k=1}^{\infty}\frac{k!\exp(k)}{(k+1)^k}$

Steffensen's method. Consider the iteration formula $x_{n+1}=x_n-f(x_n)/g(x_n)$ where $g(x)=[f(x+f(x))-f(x)]/f(x)$. Show that this quadratically

Is there a sequence of unbounded closed intervals such that its intersection is empty?

Set $\{x | f(x) = \infty\}$ is of measure 0.

Under what circumstances is this function continuous?

If $f(x) = { x^2 \sin \frac 1 x \text{ for } 0 < x \leq 1}$ and $f(0)=0$, prove $f$ is rectifiable.

Prove that $\sum\limits_{k=1}^{n}\frac{|z_{k}|^2}{|z_{k+1}-z_{k}|^2}\ge 1$ for complex numbers $z_k$'s

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