Question

Proving that ${n+3\choose 3} =\frac{n+2}{2}\sum_{k=1}^{n+1}\csc^2\frac{k\pi}{n+2}$

score 219 · Answer 1 · 2026-03-30 10:13:10

219

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Proving that ${n+3\choose 3} =\frac{n+2}{2}\sum_{k=1}^{n+1}\csc^2\frac{k\pi}{n+2}$

Published on 30 Mar 2026 - 10:13

score 312 · Answer 2 · 2026-03-25 06:21:40

312

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Multiplicative functions and the sum of all divisors: $\sum_{d\mid2020}{\sigma(d)}$

Published on 25 Mar 2026 - 6:21

score 49 · Answer 3 · 2019-06-02 09:47:56

49

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Find the value of the p for which the series converges

Published on 02 Jun 2019 - 9:47

score 39 · Answer 4 · 2019-06-03 07:28:32

39

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ration of $M/N$ in $2$ alternating series

Published on 03 Jun 2019 - 7:28

score 328 · Answer 5 · 2026-03-30 10:13:19

328

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Alternating sum of binomial coefficients multiplied by index to an n-2 extent

Published on 30 Mar 2026 - 10:13

score 24 · Answer 6 · 2019-06-03 20:12:24

24

Views

Prove that even decomposition maximizes $\sqrt{x}\ln x$

Published on 03 Jun 2019 - 20:12

score 353 · Answer 7 · 2026-03-27 00:02:12

353

Views

Proof by induction for nth derivative

Published on 27 Mar 2026 - 0:02

score 62 · Answer 8 · 2026-03-26 01:02:37

62

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How to express this summation?

Published on 26 Mar 2026 - 1:02

score 55 · Answer 9 · 2019-06-04 22:57:23

55

Views

Consider the Sequence and prove.

Published on 04 Jun 2019 - 22:57

score 30 · Answer 10 · 2026-04-03 02:12:06

30

Views

behavior at boundary of convergence

Published on 03 Apr 2026 - 2:12

score 226 · Answer 11 · 2026-03-25 12:30:32

226

Views

Proof by induction summation

Published on 25 Mar 2026 - 12:30

score 54 · Answer 12 · 2026-03-27 20:12:53

54

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How to simplify this expression with fractions?

Published on 27 Mar 2026 - 20:12

score 21 · Answer 13 · 2026-03-29 10:49:10

21

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Showing that the number of non-null elements of an unconditionally Cauchy family is countable

Published on 29 Mar 2026 - 10:49

score 80 · Answer 14 · 2026-03-25 04:42:35

80

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Can someone explain to me how $\sum_{k=1}^\infty \frac{n}{(n+k)(n+k+1)}=\frac{n}{n+1}$?

Published on 25 Mar 2026 - 4:42

score 2.5k · Answer 15 · 2026-03-25 23:42:14

2.5k

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Prove by induction that $\sum _{r=1}^n \cos((2r-1)\theta) = \frac{\sin(2n\theta)}{2\sin\theta}$ is true $\forall \ n \in \mathbb{Z^+}$

Published on 25 Mar 2026 - 23:42

List Question

Proving that ${n+3\choose 3} =\frac{n+2}{2}\sum_{k=1}^{n+1}\csc^2\frac{k\pi}{n+2}$

Multiplicative functions and the sum of all divisors: $\sum_{d\mid2020}{\sigma(d)}$

Find the value of the p for which the series converges

ration of $M/N$ in $2$ alternating series

Alternating sum of binomial coefficients multiplied by index to an n-2 extent

Prove that even decomposition maximizes $\sqrt{x}\ln x$

Proof by induction for nth derivative

How to express this summation?

Consider the Sequence and prove.

behavior at boundary of convergence

Proof by induction summation

How to simplify this expression with fractions?

Showing that the number of non-null elements of an unconditionally Cauchy family is countable

Can someone explain to me how $\sum_{k=1}^\infty \frac{n}{(n+k)(n+k+1)}=\frac{n}{n+1}$?

Prove by induction that $\sum _{r=1}^n \cos((2r-1)\theta) = \frac{\sin(2n\theta)}{2\sin\theta}$ is true $\forall \ n \in \mathbb{Z^+}$

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