Question

Convergence of local Newton method for $f(x) = x^4+x^2$

score 61 · Answer 1 · 2026-04-13 01:34:01

61

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Convergence of local Newton method for $f(x) = x^4+x^2$

Published on 13 Apr 2026 - 1:34

score 203 · Answer 2 · 2026-04-11 16:56:14

203

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Does convergence for Cauchy sequence fail only when the limit is not in the domain?

Published on 11 Apr 2026 - 16:56

score 577 · Answer 3 · 2026-04-15 11:10:45

577

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Show that $\ell^1$ is non complete under $\ell^2$ norm

Published on 15 Apr 2026 - 11:10

score 42 · Answer 4 · 2026-04-17 13:49:43

42

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Proving $X_m \xrightarrow{a.s.}0$, when $X_m \le x_mV^2$and $X_m \xrightarrow{p}0$, $x_mV^2 \xrightarrow{d}xV^2$ where $V\sim \mathcal{N}(0,\sigma^2)$

Published on 17 Apr 2026 - 13:49

score 145 · Answer 5 · 2026-04-15 08:15:00

145

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show that $S_n$ diverges a.s. and in $L^2$.

Published on 15 Apr 2026 - 8:15

score 84 · Answer 6 · 2026-04-15 23:55:19

84

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Determine whether the improper integral $\int_{1}^{\infty} \frac{1}{x^3\sqrt{x^2 -1}} dx$ converges

Published on 15 Apr 2026 - 23:55

score 106 · Answer 7 · 2026-04-08 21:58:59

106

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Convergence of continued fractions with negative decreasing terms

Published on 08 Apr 2026 - 21:58

score 82 · Answer 8 · 2026-04-15 02:52:22

82

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Proving $\lim_{n \to \infty} \left(2x^{\frac{1}{n}}-1\right)^{n}=x^2$

Published on 15 Apr 2026 - 2:52

score 496 · Answer 9 · 2026-04-17 00:49:36

496

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Suppose $\{x_n\}$ is bounded. Prove $\frac{x_n}{n^k} \rightarrow 0$, as $n \rightarrow \infty$, for all $k \in \mathbb{N}$.

Published on 17 Apr 2026 - 0:49

score 390 · Answer 10 · 2026-04-16 13:26:24

390

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What is the radius of convergence for the Taylor expansion of $\frac{e^x\sin(x)}{x^2+25}$ about $x=0$?

Published on 16 Apr 2026 - 13:26

score 146 · Answer 11 · 2026-04-12 21:32:08

146

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Is there any statistically convergent real sequence, which is not almost convergent?

Published on 12 Apr 2026 - 21:32

score 62 · Answer 12 · 2026-04-16 17:06:21

62

Views

On convergence in $L^p$

Published on 16 Apr 2026 - 17:06

score 24 · Answer 13 · 2026-03-26 14:30:28

24

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If $f$ is invertible in $A \subset M$, $\lim_n \sum_{x \in f^{-1}(y)} g_n (y) = \chi_{f(A)}(y)$?

Published on 26 Mar 2026 - 14:30

score 102 · Answer 14 · 2026-04-15 03:44:45

102

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How to determing the convergence of $\sum_{x=1}^\infty (e-(1+\frac{1}{x})^x)$?

Published on 15 Apr 2026 - 3:44

score 77 · Answer 15 · 2026-04-15 06:31:25

77

Views

Prove that $1-e^{-e^{-c}} \sim e^{-c}$

Published on 15 Apr 2026 - 6:31

List Question

Convergence of local Newton method for $f(x) = x^4+x^2$

Does convergence for Cauchy sequence fail only when the limit is not in the domain?

Show that $\ell^1$ is non complete under $\ell^2$ norm

Proving $X_m \xrightarrow{a.s.}0$, when $X_m \le x_mV^2$and $X_m \xrightarrow{p}0$, $x_mV^2 \xrightarrow{d}xV^2$ where $V\sim \mathcal{N}(0,\sigma^2)$

show that $S_n$ diverges a.s. and in $L^2$.

Determine whether the improper integral $\int_{1}^{\infty} \frac{1}{x^3\sqrt{x^2 -1}} dx$ converges

Convergence of continued fractions with negative decreasing terms

Proving $\lim_{n \to \infty} \left(2x^{\frac{1}{n}}-1\right)^{n}=x^2$

Suppose $\{x_n\}$ is bounded. Prove $\frac{x_n}{n^k} \rightarrow 0$, as $n \rightarrow \infty$, for all $k \in \mathbb{N}$.

What is the radius of convergence for the Taylor expansion of $\frac{e^x\sin(x)}{x^2+25}$ about $x=0$?

Is there any statistically convergent real sequence, which is not almost convergent?

On convergence in $L^p$

If $f$ is invertible in $A \subset M$, $\lim_n \sum_{x \in f^{-1}(y)} g_n (y) = \chi_{f(A)}(y)$?

How to determing the convergence of $\sum_{x=1}^\infty (e-(1+\frac{1}{x})^x)$?

Prove that $1-e^{-e^{-c}} \sim e^{-c}$

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