Question

Splitting up compound inequalities of multiple variables

score 161 · Answer 1 · 2018-12-27 20:21:39

161

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Splitting up compound inequalities of multiple variables

Published on 27 Dec 2018 - 20:21

score 112 · Answer 2 · 2026-03-28 14:06:34

112

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How to solve $1+\sum_{k=1}^r 3^k\binom{n}{k}$ (using, say, $ S\{n\} = \frac{a_1(1-r^n)}{1-r} $) so I can use it for large $r$?

Published on 28 Mar 2026 - 14:06

score 87 · Answer 3 · 2018-12-28 19:43:06

87

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Is there a closed form of $\sum_{k=1}^{\infty}\frac{\sin (2k-1)\pi x}{(2k-1)^5\pi^5}$

Published on 28 Dec 2018 - 19:43

score 92 · Answer 4 · 2026-03-25 04:38:46

92

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How has this Chebyshev expansion been reindexed?

Published on 25 Mar 2026 - 4:38

score 52 · Answer 5 · 2026-03-25 09:29:54

52

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Looking for the name and properties of ${\varphi}_{2} (r, N) = \sum_{- N \le s, t \le N, (r, s, t) = 1} 1$ and $\sum_{d \mid r} \mu (d)/d^2$

Published on 25 Mar 2026 - 9:29

score 77 · Answer 6 · 2026-03-29 08:18:31

77

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Why is there a $m-1$ when approximating a lower bound of a function through summation or integral?

Published on 29 Mar 2026 - 8:18

score 1.4k · Answer 7 · 2026-03-27 19:08:25

1.4k

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New Year Maths $2019$

Published on 27 Mar 2026 - 19:08

score 115 · Answer 8 · 2018-12-31 15:47:29

115

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Evaluate $\sum_{r=2}^{\infty} \frac{2-r}{r(r+1)(r+2)}$

Published on 31 Dec 2018 - 15:47

score 458 · Answer 9 · 2026-03-27 13:01:58

458

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Prove: $\lim_{n\to\infty}{\sum_{m=0}^{n}{\sum_{k=0}^{n-m}{\frac{2^{n-m-k}}{n-m+1}\,\frac{{{2k}\choose{k}}{{2m}\choose{m}}}{{{2n}\choose{n}}}}}}=\pi$

Published on 27 Mar 2026 - 13:01

score 87 · Answer 10 · 2018-12-31 21:37:07

87

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If $\sum_{n=1}^{\infty} \sum_{k=1}^{\infty} f_{n}(k) = \infty$ then $\sum_{k=1}^{\infty} \sum_{n=1}^{\infty} f_{n}(k) = \infty$.

Published on 31 Dec 2018 - 21:37

score 30 · Answer 11 · 2019-01-01 08:53:16

30

Views

Summation with power

Published on 01 Jan 2019 - 8:53

score 142 · Answer 12 · 2019-01-01 09:54:21

142

Views

How to show that these two summations are equal

Published on 01 Jan 2019 - 9:54

score 118 · Answer 13 · 2026-03-26 06:27:48

118

Views

Finding $\limsup_{n\to\infty}\sum_{k=0}^n(-1)^k|\sin k|$

Published on 26 Mar 2026 - 6:27

score 182 · Answer 14 · 2026-03-25 11:02:46

182

Views

find the first term of the series?

Published on 25 Mar 2026 - 11:02

score 304 · Answer 15 · 2026-03-25 19:01:25

304

Views

Using a gamblers race to approximate $\pi$

Published on 25 Mar 2026 - 19:01

List Question

Splitting up compound inequalities of multiple variables

How to solve $1+\sum_{k=1}^r 3^k\binom{n}{k}$ (using, say, $ S\{n\} = \frac{a_1(1-r^n)}{1-r} $) so I can use it for large $r$?

Is there a closed form of $\sum_{k=1}^{\infty}\frac{\sin (2k-1)\pi x}{(2k-1)^5\pi^5}$

How has this Chebyshev expansion been reindexed?

Looking for the name and properties of ${\varphi}_{2} (r, N) = \sum_{- N \le s, t \le N, (r, s, t) = 1} 1$ and $\sum_{d \mid r} \mu (d)/d^2$

Why is there a $m-1$ when approximating a lower bound of a function through summation or integral?

New Year Maths $2019$

Evaluate $\sum_{r=2}^{\infty} \frac{2-r}{r(r+1)(r+2)}$

Prove: $\lim_{n\to\infty}{\sum_{m=0}^{n}{\sum_{k=0}^{n-m}{\frac{2^{n-m-k}}{n-m+1}\,\frac{{{2k}\choose{k}}{{2m}\choose{m}}}{{{2n}\choose{n}}}}}}=\pi$

If $\sum_{n=1}^{\infty} \sum_{k=1}^{\infty} f_{n}(k) = \infty$ then $\sum_{k=1}^{\infty} \sum_{n=1}^{\infty} f_{n}(k) = \infty$.

Summation with power

How to show that these two summations are equal

Finding $\limsup_{n\to\infty}\sum_{k=0}^n(-1)^k|\sin k|$

find the first term of the series?

Using a gamblers race to approximate $\pi$

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