Question

Proving $\sum\limits_{k=1}^{N-1}\left[\frac{\sin\left(\frac{\pi km}{N}\right)}{\sin\left(\frac{\pi k}{N}\right)}\right]^{2}=m(N-m)$

score 162 · Answer 1 · 2026-03-26 06:34:55

162

Views

Proving $\sum\limits_{k=1}^{N-1}\left[\frac{\sin\left(\frac{\pi km}{N}\right)}{\sin\left(\frac{\pi k}{N}\right)}\right]^{2}=m(N-m)$

Published on 26 Mar 2026 - 6:34

score 42 · Answer 2 · 2026-04-09 02:55:12

42

Views

Limits of infinite series

Published on 09 Apr 2026 - 2:55

score 46 · Answer 3 · 2019-09-21 16:27:47

46

Views

Summation or Algebra?

Published on 21 Sep 2019 - 16:27

score 79 · Answer 4 · 2026-04-08 20:36:58

79

Views

Alternate Sum of Cubes Using Identity

Published on 08 Apr 2026 - 20:36

score 195 · Answer 5 · 2026-03-27 13:01:59

195

Views

Prove that $\frac{\sqrt[n]{\prod_{k = 1}^nx_n}}{m} \ge n - 1$ where $\sum_{k = 1}^n\frac{1}{x_k + m} = \frac{1}{m}$.

Published on 27 Mar 2026 - 13:01

score 189.9k · Answer 6 · 2019-09-23 17:26:28

189.9k

Views

Sum of 1 + 1/2 + 1/3 +.... + 1/n

Published on 23 Sep 2019 - 17:26

score 41 · Answer 7 · 2026-03-26 16:04:58

41

Views

Representation of $n$-th derivative as the sum

Published on 26 Mar 2026 - 16:04

score 35 · Answer 8 · 2026-04-02 23:17:46

35

Views

Exponential function in which all solutions add up to a certain number

Published on 02 Apr 2026 - 23:17

score 39 · Answer 9 · 2026-03-26 03:18:58

39

Views

Name for this power sum formula?

Published on 26 Mar 2026 - 3:18

score 56 · Answer 10 · 2026-03-26 21:25:25

56

Views

Where's the error in this "proof"?

Published on 26 Mar 2026 - 21:25

score 962 · Answer 11 · 2026-03-25 03:07:40

962

Views

What is the reasoning behind changing the order of summation in this example?

Published on 25 Mar 2026 - 3:07

score 90 · Answer 12 · 2026-03-29 18:33:32

90

Views

Equation to determine if a natural number is a prime, not a prime, summation or power of 2

Published on 29 Mar 2026 - 18:33

score 41 · Answer 13 · 2026-03-25 06:50:36

41

Views

How is the last step of this sum derived?

Published on 25 Mar 2026 - 6:50

score 112 · Answer 14 · 2026-03-28 04:42:15

112

Views

Simplify the following expression $\sum_{j=0}^n 2^n \binom{1/2}{n-j}\binom{j-1/2}{j}$

Published on 28 Mar 2026 - 4:42

score 95 · Answer 15 · 2026-03-26 06:21:15

95

Views

A pattern on finding squares for which their sum is $\Big(\sum\limits_{i=0}^j x^i\Big)^2$

Published on 26 Mar 2026 - 6:21

List Question

Proving $\sum\limits_{k=1}^{N-1}\left[\frac{\sin\left(\frac{\pi km}{N}\right)}{\sin\left(\frac{\pi k}{N}\right)}\right]^{2}=m(N-m)$

Limits of infinite series

Summation or Algebra?

Alternate Sum of Cubes Using Identity

Prove that $\frac{\sqrt[n]{\prod_{k = 1}^nx_n}}{m} \ge n - 1$ where $\sum_{k = 1}^n\frac{1}{x_k + m} = \frac{1}{m}$.

Sum of 1 + 1/2 + 1/3 +.... + 1/n

Representation of $n$-th derivative as the sum

Exponential function in which all solutions add up to a certain number

Name for this power sum formula?

Where's the error in this "proof"?

What is the reasoning behind changing the order of summation in this example?

Equation to determine if a natural number is a prime, not a prime, summation or power of 2

How is the last step of this sum derived?

Simplify the following expression $\sum_{j=0}^n 2^n \binom{1/2}{n-j}\binom{j-1/2}{j}$

A pattern on finding squares for which their sum is $\Big(\sum\limits_{i=0}^j x^i\Big)^2$

Trending Questions

Popular # Hahtags

Popular Questions