Question

Divergence of sequence $y_n=(1-x_1)(1-\ x_2)\cdots(1-x_n)$ if $x_{n+1}=(x_{n+1}+1)x_n$

score 95 · Answer 1 · 2026-04-17 14:33:35

95

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Divergence of sequence $y_n=(1-x_1)(1-\ x_2)\cdots(1-x_n)$ if $x_{n+1}=(x_{n+1}+1)x_n$

Published on 17 Apr 2026 - 14:33

score 195 · Answer 2 · 2026-04-12 07:03:24

195

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Is there a generating function for this sequence?

Published on 12 Apr 2026 - 7:03

score 593 · Answer 3 · 2026-04-17 05:22:19

593

Views

Determine if the sequence converges or diverges

Published on 17 Apr 2026 - 5:22

score 401 · Answer 4 · 2026-04-08 14:50:10

401

Views

Fourier series with "Riemann" coefficients

Published on 08 Apr 2026 - 14:50

score 158 · Answer 5 · 2026-04-14 03:42:26

158

Views

If the limit of a series is 0 and it is decreasing does it also converge ?

Published on 14 Apr 2026 - 3:42

score 68 · Answer 6 · 2026-03-25 17:43:52

68

Views

Infinite series involving binomial and geometric

Published on 25 Mar 2026 - 17:43

score 103 · Answer 7 · 2026-04-16 06:29:34

103

Views

Radius and interval of convergence for $\sum \limits_{n=1}^\infty \frac{x^{n^2}}{2^n}$

Published on 16 Apr 2026 - 6:29

score 44 · Answer 8 · 2026-04-17 08:17:42

44

Views

Find $x_n$ such that $ \exp(- \sqrt{2 \log n} x_n - x_{n}^{2}/2) = (\sqrt{ 2 \log n} + x_n) \sqrt{2 \pi}$

Published on 17 Apr 2026 - 8:17

score 215 · Answer 9 · 2026-04-12 15:09:09

215

Views

Beautiful sum of trigonometric roots

Published on 12 Apr 2026 - 15:09

score 67 · Answer 10 · 2026-04-15 13:04:20

67

Views

How to show $y_k = \sum\limits_{i = 0}^{k-1} e^{-y_i}$ diverges as $k \to \infty$

Published on 15 Apr 2026 - 13:04

score 199 · Answer 11 · 2026-04-14 17:48:13

199

Views

Elementary proof of $\sum_{k=1}^{n}\frac{1}{2k+1}$ with all odd denominators is never an integer?

Published on 14 Apr 2026 - 17:48

score 16 · Answer 12 · 2026-04-14 23:00:03

16

Views

Given Set of Probabilities of Gaussian Distribution, How to Find Best Treshold and Maximum F1 Score?

Published on 14 Apr 2026 - 23:00

score 166 · Answer 13 · 2026-04-15 10:38:35

166

Views

How many limit points does $\sin^2(\pi n/2)+(-1)^n/{\pi n} $ have?

Published on 15 Apr 2026 - 10:38

score 80 · Answer 14 · 2026-04-17 13:45:16

80

Views

Doubt Regarding Termwise differentiation of Fourier Series

Published on 17 Apr 2026 - 13:45

score 653 · Answer 15 · 2026-04-16 14:47:59

653

Views

What's the supremum of $\left\{(-1)^n(1-\frac{1}{n^2}): n \in \mathbb{N}\right\}$?

Published on 16 Apr 2026 - 14:47

List Question

Divergence of sequence $y_n=(1-x_1)(1-\ x_2)\cdots(1-x_n)$ if $x_{n+1}=(x_{n+1}+1)x_n$

Is there a generating function for this sequence?

Determine if the sequence converges or diverges

Fourier series with "Riemann" coefficients

If the limit of a series is 0 and it is decreasing does it also converge ?

Infinite series involving binomial and geometric

Radius and interval of convergence for $\sum \limits_{n=1}^\infty \frac{x^{n^2}}{2^n}$

Find $x_n$ such that $ \exp(- \sqrt{2 \log n} x_n - x_{n}^{2}/2) = (\sqrt{ 2 \log n} + x_n) \sqrt{2 \pi}$

Beautiful sum of trigonometric roots

How to show $y_k = \sum\limits_{i = 0}^{k-1} e^{-y_i}$ diverges as $k \to \infty$

Elementary proof of $\sum_{k=1}^{n}\frac{1}{2k+1}$ with all odd denominators is never an integer?

Given Set of Probabilities of Gaussian Distribution, How to Find Best Treshold and Maximum F1 Score?

How many limit points does $\sin^2(\pi n/2)+(-1)^n/{\pi n} $ have?

Doubt Regarding Termwise differentiation of Fourier Series

What's the supremum of $\left\{(-1)^n(1-\frac{1}{n^2}): n \in \mathbb{N}\right\}$?

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