Question

Real life applications of Cauchy Sequences?

score 2.5k · Answer 1 · 2026-04-10 17:48:48

2.5k

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Real life applications of Cauchy Sequences?

Published on 10 Apr 2026 - 17:48

score 692 · Answer 2 · 2026-04-16 04:57:27

692

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Define $x_0=0$ and $x_{n+1}=x_n-[(\tan x_n-1)/\sec^2x_n]$. What is $\lim_{n\to \infty}x_n$ in this example? Relate this to Newton's method.

Published on 16 Apr 2026 - 4:57

score 83 · Answer 3 · 2026-04-15 17:50:14

83

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solve $a_n=a_{n-1}^2-\lambda, a_0=\beta$

Published on 15 Apr 2026 - 17:50

score 98 · Answer 4 · 2026-04-11 17:49:53

98

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Calculating $\inf \left\{\exp((-1)^nn)\right\}$ via the $\epsilon$-definition?

Published on 11 Apr 2026 - 17:49

score 1.1k · Answer 5 · 2026-04-13 07:45:01

1.1k

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Devise a Newton iteration formula for computing $\sqrt[3]{R}$ where $R>0$. Perform a graphical analysis of your function $f(x)$ to determine

Published on 13 Apr 2026 - 7:45

score 27 · Answer 6 · 2026-04-12 14:41:30

27

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Showing that a piece-wise defined sequence converges to $0$ via $\epsilon$-definition?

Published on 12 Apr 2026 - 14:41

score 39 · Answer 7 · 2026-04-14 03:47:52

39

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Proof Verification and Help: Proving $b^n$ converges to $0$

Published on 14 Apr 2026 - 3:47

score 50 · Answer 8 · 2026-04-17 04:43:49

50

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Find the limit of $\ x_n^{\ a_n} - x_n^{\ b_n}$?

Published on 17 Apr 2026 - 4:43

score 34 · Answer 9 · 2026-04-10 19:08:54

34

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Is it possible to get common difference from the output of floor function?

Published on 10 Apr 2026 - 19:08

score 181 · Answer 10 · 2026-04-17 07:26:06

181

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Is there any known value of the infinite sum $\sum_{m=1,n=1}^\infty \frac{1}{(m^2+n^2)^2}$?

Published on 17 Apr 2026 - 7:26

score 103 · Answer 11 · 2026-04-15 03:17:59

103

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Prove sequences {$a_n$} {$b_n$} of complex numbers converge

Published on 15 Apr 2026 - 3:17

score 1.7k · Answer 12 · 2026-04-15 18:50:14

1.7k

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Alternating harmonic series convergence $S_n = 1-\frac12 + \frac13 - \cdots + (-1)^n\frac1n$

Published on 15 Apr 2026 - 18:50

score 225 · Answer 13 · 2026-04-17 13:22:28

225

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Find the smallest value of $x$ such that the sequence converges to $0$.

Published on 17 Apr 2026 - 13:22

score 450 · Answer 14 · 2026-04-09 09:27:43

450

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Solving this quant interview question

Published on 09 Apr 2026 - 9:27

score 74 · Answer 15 · 2026-04-14 21:02:44

74

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Showing that the series $\sum 3^{-k}{\sqrt{1-e^{-k}}}$ converges.

Published on 14 Apr 2026 - 21:02

List Question

Real life applications of Cauchy Sequences?

Define $x_0=0$ and $x_{n+1}=x_n-[(\tan x_n-1)/\sec^2x_n]$. What is $\lim_{n\to \infty}x_n$ in this example? Relate this to Newton's method.

solve $a_n=a_{n-1}^2-\lambda, a_0=\beta$

Calculating $\inf \left\{\exp((-1)^nn)\right\}$ via the $\epsilon$-definition?

Devise a Newton iteration formula for computing $\sqrt[3]{R}$ where $R>0$. Perform a graphical analysis of your function $f(x)$ to determine

Showing that a piece-wise defined sequence converges to $0$ via $\epsilon$-definition?

Proof Verification and Help: Proving $b^n$ converges to $0$

Find the limit of $\ x_n^{\ a_n} - x_n^{\ b_n}$?

Is it possible to get common difference from the output of floor function?

Is there any known value of the infinite sum $\sum_{m=1,n=1}^\infty \frac{1}{(m^2+n^2)^2}$?

Prove sequences {$a_n$} {$b_n$} of complex numbers converge

Alternating harmonic series convergence $S_n = 1-\frac12 + \frac13 - \cdots + (-1)^n\frac1n$

Find the smallest value of $x$ such that the sequence converges to $0$.

Solving this quant interview question

Showing that the series $\sum 3^{-k}{\sqrt{1-e^{-k}}}$ converges.

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