Question

Finding a formula for $(1^3)\cdot(n)+(2^3)\cdot(n-1)+(3^3)\cdot(n-2)+ \cdots + (n^3)\cdot(1)$

score 81 · Answer 1 · 2026-03-25 06:12:46

81

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Finding a formula for $(1^3)\cdot(n)+(2^3)\cdot(n-1)+(3^3)\cdot(n-2)+ \cdots + (n^3)\cdot(1)$

Published on 25 Mar 2026 - 6:12

score 106 · Answer 2 · 2026-04-02 13:42:59

106

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Is $\sum_{k=0}^n \left(k+1\right)\left(C^n_k\right)^2 = \frac{n+2}{2} C^{2n}_n$ for any positive integer $n$?

Published on 02 Apr 2026 - 13:42

score 19 · Answer 3 · 2019-08-24 15:16:35

19

Views

Expectation value summation

Published on 24 Aug 2019 - 15:16

score 144 · Answer 4 · 2026-03-27 07:39:30

144

Views

Solving Basel Problem using euler infinite product and infinite product-sum equality

Published on 27 Mar 2026 - 7:39

score 60 · Answer 5 · 2019-08-24 22:23:31

60

Views

The expansion of $a_n=(1+\frac{1}{n})^n$ and the proof of the limit.

Published on 24 Aug 2019 - 22:23

score 566 · Answer 6 · 2019-08-25 09:40:36

566

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A nice Combinatorial Identity

Published on 25 Aug 2019 - 9:40

score 334 · Answer 7 · 2019-08-25 09:48:32

334

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The value of $\sum _{n=1}^{\infty }{\left(q\right)^n\left(\sin(na)\right), |q|<1}$

Published on 25 Aug 2019 - 9:48

score 66 · Answer 8 · 2019-08-25 10:48:42

66

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Closed form for $\sum_{n=1}^{m} n^n$

Published on 25 Aug 2019 - 10:48

score 64 · Answer 9 · 2026-04-08 18:31:58

64

Views

How to put an expression in terms of a sum or a "productory"

Published on 08 Apr 2026 - 18:31

score 79 · Answer 10 · 2019-08-26 17:32:59

79

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To find closed form of given sum

Published on 26 Aug 2019 - 17:32

score 53 · Answer 11 · 2019-08-27 09:02:51

53

Views

sum of $\lim \limits_{n \to \infty}\big(\frac{1}{2n}+\frac{1}{2n+1}+\cdots+\frac{1}{3n-2}+\frac{1}{3n-1}\big)$

Published on 27 Aug 2019 - 9:02

score 105 · Answer 12 · 2026-03-28 02:48:42

105

Views

Expressing a Binomial Series as an Integral

Published on 28 Mar 2026 - 2:48

score 55 · Answer 13 · 2026-04-03 01:45:41

55

Views

Asymptotics of a double sum after perturbation

Published on 03 Apr 2026 - 1:45

score 60 · Answer 14 · 2026-04-04 20:42:43

60

Views

What does $\sup _{n \in \mathbb{N}} \sum_{j, k=0}^{n}\left|x_{j k}\right|<\infty$ mean in the context of double series?

Published on 04 Apr 2026 - 20:42

score 815 · Answer 15 · 2026-04-03 01:49:09

815

Views

Summation of fractional parts of $x/n$

Published on 03 Apr 2026 - 1:49

List Question

Finding a formula for $(1^3)\cdot(n)+(2^3)\cdot(n-1)+(3^3)\cdot(n-2)+ \cdots + (n^3)\cdot(1)$

Is $\sum_{k=0}^n \left(k+1\right)\left(C^n_k\right)^2 = \frac{n+2}{2} C^{2n}_n$ for any positive integer $n$?

Expectation value summation

Solving Basel Problem using euler infinite product and infinite product-sum equality

The expansion of $a_n=(1+\frac{1}{n})^n$ and the proof of the limit.

A nice Combinatorial Identity

The value of $\sum _{n=1}^{\infty }{\left(q\right)^n\left(\sin(na)\right), |q|<1}$

Closed form for $\sum_{n=1}^{m} n^n$

How to put an expression in terms of a sum or a "productory"

To find closed form of given sum

sum of $\lim \limits_{n \to \infty}\big(\frac{1}{2n}+\frac{1}{2n+1}+\cdots+\frac{1}{3n-2}+\frac{1}{3n-1}\big)$

Expressing a Binomial Series as an Integral

Asymptotics of a double sum after perturbation

What does $\sup _{n \in \mathbb{N}} \sum_{j, k=0}^{n}\left|x_{j k}\right|<\infty$ mean in the context of double series?

Summation of fractional parts of $x/n$

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