Question

Sums of binomials with increasing powers

score 53 · Answer 1 · 2026-04-10 13:48:13

53

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Sums of binomials with increasing powers

Published on 10 Apr 2026 - 13:48

score 1.2k · Answer 2 · 2026-04-13 04:35:18

1.2k

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Why does $\sum \frac{1}{n^{1 + \epsilon}}$ converge?

Published on 13 Apr 2026 - 4:35

score 41 · Answer 3 · 2026-04-15 18:53:14

Summation for $\sum_{n_1\geq 1}\sum_{n_2\geq 1}\sum_{n_3\geq 1} \frac{\cos 2\pi n_1x_1\cos 2\pi n_2x_2\cos 2\pi n_3x_3}{n_1^2+n_2^2+n_3^2} $

score 48 · Answer 4 · 2026-04-10 23:37:37

48

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Confusion about Geometric Series

Published on 10 Apr 2026 - 23:37

score 114 · Answer 5 · 2026-04-15 14:23:09

114

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Proving that $\sum_{n=0}^\infty \sum_{k=0}^n \frac{(-1)^n}{(k+1)\times (n-k+1)}$ converges

Published on 15 Apr 2026 - 14:23

score 39 · Answer 6 · 2026-04-09 02:22:24

39

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Summation with two costs

Published on 09 Apr 2026 - 2:22

score 45 · Answer 7 · 2026-04-10 23:52:22

45

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How to prove that a non-positive series converges?

Published on 10 Apr 2026 - 23:52

score 44 · Answer 8 · 2026-04-14 21:04:34

44

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Simplifying a finite double summation $\sum_{j=1}^n\sum_{i=1}^nf(n-ij)$ with both indexes over the same range

Published on 14 Apr 2026 - 21:04

score 65 · Answer 9 · 2026-04-15 00:01:46

65

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Show that a the sum function of a power series is differentiable twice and that $f''(x) = \frac{1}{49-7x}$

Published on 15 Apr 2026 - 0:01

score 303 · Answer 10 · 2026-04-11 22:14:17

303

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Dini's theorem, under which conditions?

Published on 11 Apr 2026 - 22:14

score 32 · Answer 11 · 2026-04-14 11:47:38

32

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$\sum_{\alpha=0}^A\binom{A}{\alpha}(zb)^{\alpha} c^{A-\alpha} = (bz+c)^A$

Published on 14 Apr 2026 - 11:47

score 77 · Answer 12 · 2026-04-12 02:04:59

77

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Can this product of sigma sums be reduced further

Published on 12 Apr 2026 - 2:04

score 67 · Answer 13 · 2026-04-12 19:40:18

67

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Computing the sum of an alternating power series

Published on 12 Apr 2026 - 19:40

score 343 · Answer 14 · 2026-04-17 01:05:59

343

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A nice combinatorial identity: $\sum_{k=1}^{n-1}\frac{\binom{k-1}{n-k-1}+\binom{k}{n-k-1}}{\binom nk}=1$

Published on 17 Apr 2026 - 1:05

score 55 · Answer 15 · 2026-04-14 10:34:15

How to show that $\sum_{i=1}^{k}\sum_{j=0}^{n-1}x_{i,j}^{2} = \frac{k}{n}$ iff $x_{i,j}=\frac{1}{n} \forall i,j$ when $\sum_{j=0}^{n-1}x_{i,j}=1$

List Question

Sums of binomials with increasing powers

Why does $\sum \frac{1}{n^{1 + \epsilon}}$ converge?

Summation for $\sum_{n_1\geq 1}\sum_{n_2\geq 1}\sum_{n_3\geq 1} \frac{\cos 2\pi n_1x_1\cos 2\pi n_2x_2\cos 2\pi n_3x_3}{n_1^2+n_2^2+n_3^2} $

Confusion about Geometric Series

Proving that $\sum_{n=0}^\infty \sum_{k=0}^n \frac{(-1)^n}{(k+1)\times (n-k+1)}$ converges

Summation with two costs

How to prove that a non-positive series converges?

Simplifying a finite double summation $\sum_{j=1}^n\sum_{i=1}^nf(n-ij)$ with both indexes over the same range

Show that a the sum function of a power series is differentiable twice and that $f''(x) = \frac{1}{49-7x}$

Dini's theorem, under which conditions?

$\sum_{\alpha=0}^A\binom{A}{\alpha}(zb)^{\alpha} c^{A-\alpha} = (bz+c)^A$

Can this product of sigma sums be reduced further

Computing the sum of an alternating power series

A nice combinatorial identity: $\sum_{k=1}^{n-1}\frac{\binom{k-1}{n-k-1}+\binom{k}{n-k-1}}{\binom nk}=1$

How to show that $\sum_{i=1}^{k}\sum_{j=0}^{n-1}x_{i,j}^{2} = \frac{k}{n}$ iff $x_{i,j}=\frac{1}{n} \forall i,j$ when $\sum_{j=0}^{n-1}x_{i,j}=1$

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