Question

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

score 79 · Answer 1 · 2026-02-23 08:25:17

79

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

Published on 23 Feb 2026 - 8:25

score 43 · Answer 2 · 2026-02-23 08:24:59

43

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Attempt at proving uniform convergence of a sum

Published on 23 Feb 2026 - 8:24

score 82 · Answer 3 · 2026-02-23 08:23:26

82

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What does this infinite series converge to?

Published on 23 Feb 2026 - 8:23

score 38 · Answer 4 · 2026-02-23 08:23:00

38

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Not all black and white?

Published on 23 Feb 2026 - 8:23

score 50 · Answer 5 · 2026-02-23 08:23:30

50

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Harmonic series and its alternating counterpart

Published on 23 Feb 2026 - 8:23

score 228 · Answer 6 · 2026-02-23 08:28:34

228

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

Published on 23 Feb 2026 - 8:28

score 93 · Answer 7 · 2026-02-23 08:18:52

93

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Interchanging summations over sets

Published on 23 Feb 2026 - 8:18

score 196 · Answer 8 · 2026-02-23 08:23:28

196

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Two identities involving binomial coefficients and double factorials

Published on 23 Feb 2026 - 8:23

score 105 · Answer 9 · 2026-02-23 08:28:30

105

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 23 Feb 2026 - 8:28

score 332 · Answer 10 · 2026-02-23 08:27:01

332

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 23 Feb 2026 - 8:27

score 52 · Answer 11 · 2026-02-23 08:27:03

52

Views

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

Published on 23 Feb 2026 - 8:27

score 37 · Answer 12 · 2026-02-23 08:27:43

37

Views

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

Published on 23 Feb 2026 - 8:27

score 38 · Answer 13 · 2026-02-23 08:25:57

38

Views

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

Published on 23 Feb 2026 - 8:25

score 232 · Answer 14 · 2026-02-23 08:27:03

232

Views

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

Published on 23 Feb 2026 - 8:27

score 92 · Answer 15 · 2026-02-23 08:28:35

92

Views

Find an alternating cycle in a graph with perfect matching.

Published on 23 Feb 2026 - 8:28

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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