Question

Function equal to infinite series $\sum_{n=0}^{\infty}(-1)^n\frac{x^{2n}}{(2n+3)(2n+1)!}$

score 78 · Answer 1 · 2023-02-15 20:49:05

78

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Function equal to infinite series $\sum_{n=0}^{\infty}(-1)^n\frac{x^{2n}}{(2n+3)(2n+1)!}$

Published on 15 Feb 2023 - 20:49

score 42 · Answer 2 · 2023-02-22 01:55:10

42

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Attempt at proving uniform convergence of a sum

Published on 22 Feb 2023 - 1:55

score 81 · Answer 3 · 2023-02-24 20:29:18

81

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What does this infinite series converge to?

Published on 24 Feb 2023 - 20:29

score 37 · Answer 4 · 2023-03-06 10:00:25

37

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Not all black and white?

Published on 06 Mar 2023 - 10:00

score 49 · Answer 5 · 2023-04-02 00:19:56

49

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Harmonic series and its alternating counterpart

Published on 02 Apr 2023 - 0:19

score 227 · Answer 6 · 2023-04-14 01:35:12

227

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A curious limit for $-\frac{1}{2}$

Published on 14 Apr 2023 - 1:35

score 92 · Answer 7 · 2023-04-25 21:21:22

92

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Interchanging summations over sets

Published on 25 Apr 2023 - 21:21

score 195 · Answer 8 · 2023-05-25 13:35:08

195

Views

Two identities involving binomial coefficients and double factorials

Published on 25 May 2023 - 13:35

score 104 · Answer 9 · 2023-06-25 00:01:35

104

Views

$t(x) - t(x/2) + t(x/3) - t(x/4) + ... = 0$ implies $t(x) + t(x/2)+t(x/3)+t(x/4) = C x$?

Published on 25 Jun 2023 - 0:01

score 331 · Answer 10 · 2023-07-20 10:49:19

331

Views

If $(a_n)$ is a decreasing real sequence and $\sum a_n$ converges, then does $\sum (-1)^n n a_n\ $ converge?

Published on 20 Jul 2023 - 10:49

score 51 · Answer 11 · 2023-09-21 03:21:25

51

Views

How can we prove that this alternating summation involving fractional floor functions is non-decreasing?

Published on 21 Sep 2023 - 3:21

score 36 · Answer 12 · 2023-09-21 05:20:46

36

Views

This alternating sum of fractional floor functions over the divisors of primorial is always a non-decreasing function (the general case).

Published on 21 Sep 2023 - 5:20

score 37 · Answer 13 · 2023-09-24 08:20:53

37

Views

Simplifying $\cos(\frac{2\pi n}{3}), n \in \mathbb{Z}$ to an alternating series

Published on 24 Sep 2023 - 8:20

score 231 · Answer 14 · 2023-10-25 20:44:36

231

Views

Evaluating $ \sum\limits_{n=1}^{N-1} \frac{(-1)^n}{\sqrt{1-\cos{\frac{2\pi n}{N}}}} $

Published on 25 Oct 2023 - 20:44

score 91 · Answer 15 · 2023-10-27 05:03:44

91

Views

Find an alternating cycle in a graph with perfect matching.

Published on 27 Oct 2023 - 5:03

List Question

Function equal to infinite series $\sum_{n=0}^{\infty}(-1)^n\frac{x^{2n}}{(2n+3)(2n+1)!}$

Attempt at proving uniform convergence of a sum

What does this infinite series converge to?

Not all black and white?

Harmonic series and its alternating counterpart

A curious limit for $-\frac{1}{2}$

Interchanging summations over sets

Two identities involving binomial coefficients and double factorials

$t(x) - t(x/2) + t(x/3) - t(x/4) + ... = 0$ implies $t(x) + t(x/2)+t(x/3)+t(x/4) = C x$?

If $(a_n)$ is a decreasing real sequence and $\sum a_n$ converges, then does $\sum (-1)^n n a_n\ $ converge?

How can we prove that this alternating summation involving fractional floor functions is non-decreasing?

This alternating sum of fractional floor functions over the divisors of primorial is always a non-decreasing function (the general case).

Simplifying $\cos(\frac{2\pi n}{3}), n \in \mathbb{Z}$ to an alternating series

Evaluating $ \sum\limits_{n=1}^{N-1} \frac{(-1)^n}{\sqrt{1-\cos{\frac{2\pi n}{N}}}} $

Find an alternating cycle in a graph with perfect matching.

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