Question

A series $10^{12} + 10^7 - 45\sum_{k=1}^{999}\csc^4\frac{k\pi}{1000}.$

score 364 · Answer 1 · 2026-04-15 17:57:28

364

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A series $10^{12} + 10^7 - 45\sum_{k=1}^{999}\csc^4\frac{k\pi}{1000}.$

Published on 15 Apr 2026 - 17:57

score 115 · Answer 2 · 2026-04-25 23:56:20

115

Views

Write $x^{n-1} + x^{n-2}y + \cdots + xy^{n-2} + y^{n-1}$ using summation notation

Published on 25 Apr 2026 - 23:56

score 9.1k · Answer 3 · 2026-04-25 23:57:59

9.1k

Views

Bounds of Summation - What happens when the upper bound is below the lower bound

Published on 25 Apr 2026 - 23:57

score 159 · Answer 4 · 2026-04-11 18:06:36

159

Views

Binomial identity: Clever idea for a short proof?

Published on 11 Apr 2026 - 18:06

score 83 · Answer 5 · 2026-04-17 10:30:22

83

Views

Find sum of expressions $x_1\dotsb x_k$ where summation is over solutions for $n=x_1+\dots+x_k$

Published on 17 Apr 2026 - 10:30

score 130 · Answer 6 · 2026-04-15 18:11:32

130

Views

Prove the Result is 1/2

Published on 15 Apr 2026 - 18:11

score 65 · Answer 7 · 2026-04-14 17:43:02

65

Views

Limit and sequence involving tangent

Published on 14 Apr 2026 - 17:43

score 225 · Answer 8 · 2026-04-16 17:13:44

225

Views

Prove that $\displaystyle \sum_{1\leq k<j\leq n} \tan^2\left(\frac{k\pi}{2n+1}\right)\tan^2\left(\frac{j\pi}{2n+1}\right)=\binom{2n+1}{4} $

Published on 16 Apr 2026 - 17:13

score 8.3k · Answer 9 · 2026-04-16 15:15:19

8.3k

Views

Formula for $1^k+2^k+3^k...n^k$ for $n,k \in \mathbb{N}$

Published on 16 Apr 2026 - 15:15

score 417 · Answer 10 · 2026-04-15 22:33:02

417

Views

Find the expected value of $E[\frac{1}{\left(X+1\right)^2}]$ where X is binomial

Published on 15 Apr 2026 - 22:33

score 172 · Answer 11 · 2026-04-14 15:28:44

172

Views

Using generating functions to solve a recurrence

Published on 14 Apr 2026 - 15:28

score 5.2k · Answer 12 · 2026-04-09 20:06:07

5.2k

Views

How should I deal with zero values in a list of values to be summed/averaged?

Published on 09 Apr 2026 - 20:06

score 77 · Answer 13 · 2026-04-09 01:01:26

77

Views

Closed form for a hypergeometric sum with multiple parameters.

Published on 09 Apr 2026 - 1:01

score 115 · Answer 14 · 2026-04-14 02:29:13

115

Views

Calculate the original function from a Fourier cosine series given

Published on 14 Apr 2026 - 2:29

score 1.2k · Answer 15 · 2026-04-13 23:16:13

1.2k

Views

Intuitive reason for why $\left(\displaystyle\sum_{i=0}^n i\right)^2 = \displaystyle\sum_{i=0}^n i^3$

Published on 13 Apr 2026 - 23:16

List Question

A series $10^{12} + 10^7 - 45\sum_{k=1}^{999}\csc^4\frac{k\pi}{1000}.$

Write $x^{n-1} + x^{n-2}y + \cdots + xy^{n-2} + y^{n-1}$ using summation notation

Bounds of Summation - What happens when the upper bound is below the lower bound

Binomial identity: Clever idea for a short proof?

Find sum of expressions $x_1\dotsb x_k$ where summation is over solutions for $n=x_1+\dots+x_k$

Prove the Result is 1/2

Limit and sequence involving tangent

Prove that $\displaystyle \sum_{1\leq k<j\leq n} \tan^2\left(\frac{k\pi}{2n+1}\right)\tan^2\left(\frac{j\pi}{2n+1}\right)=\binom{2n+1}{4} $

Formula for $1^k+2^k+3^k...n^k$ for $n,k \in \mathbb{N}$

Find the expected value of $E[\frac{1}{\left(X+1\right)^2}]$ where X is binomial

Using generating functions to solve a recurrence

How should I deal with zero values in a list of values to be summed/averaged?

Closed form for a hypergeometric sum with multiple parameters.

Calculate the original function from a Fourier cosine series given

Intuitive reason for why $\left(\displaystyle\sum_{i=0}^n i\right)^2 = \displaystyle\sum_{i=0}^n i^3$

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