Question

Generating functions and central binomial coefficient

score 4.3k · Answer 1 · 2026-04-15 02:46:36

4.3k

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Generating functions and central binomial coefficient

Published on 15 Apr 2026 - 2:46

score 121 · Answer 2 · 2026-04-17 12:17:42

121

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Prove that $1+2^1+2^2+\ldots +2^n=2^{n+1}-1$ using induction

Published on 17 Apr 2026 - 12:17

score 283 · Answer 3 · 2026-04-16 12:47:40

283

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How prove this identity$\sum_{k=0}^{n}\binom{2k}{k}\binom{n+k}{2k}(s-t)^{n-k}t^k=\sum_{k=0}^{n}\binom{n}{k}^2s^{n-k}t^k$

Published on 16 Apr 2026 - 12:47

score 2.7k · Answer 4 · 2026-04-15 07:14:27

2.7k

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How to prove combinatorial identity $\sum_{k=0}^s{s\choose k}{m\choose k}{k\choose m-s}={2s\choose s}{s\choose m-s}$?

Published on 15 Apr 2026 - 7:14

score 6.7k · Answer 5 · 2026-04-11 18:48:12

6.7k

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Product of sums equal to sum of products

Published on 11 Apr 2026 - 18:48

score 4.3k · Answer 6 · 2026-04-14 17:44:23

4.3k

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Does $\sum_{n=1}^{\infty}\frac{\cos\left(\frac{n\pi}{2}\right)}{\sqrt{n}}$ converge?

Published on 14 Apr 2026 - 17:44

score 50 · Answer 7 · 2026-04-13 10:24:13

50

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Estimation of a sum independent of $n$

Published on 13 Apr 2026 - 10:24

score 345 · Answer 8 · 2026-04-13 01:52:43

345

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How to prove this Catalan number identity

Published on 13 Apr 2026 - 1:52

score 3k · Answer 9 · 2026-04-13 16:21:39

3k

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Convolution of discrete uniform distributions

Published on 13 Apr 2026 - 16:21

score 213 · Answer 10 · 2026-04-14 09:35:20

213

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Is there a summation formula for this equation (contains square roots, and functions within the square root)?

Published on 14 Apr 2026 - 9:35

score 62 · Answer 11 · 2026-04-12 10:10:00

62

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Sum of segments inside a right triangle.

Published on 12 Apr 2026 - 10:10

score 290 · Answer 12 · 2026-04-15 17:15:18

290

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Prove that $\sum_{n=0}^\infty \frac{(-1)^n}{3n+1} = \frac{\pi}{3\sqrt{3}}+\frac{\log 2}{3}$

Published on 15 Apr 2026 - 17:15

score 136 · Answer 13 · 2026-04-17 04:25:59

136

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convergence of infinite series $\sum_{n=1}^\infty \frac{x^n}{(1+x)(1+x^2)(1+x^3)\cdot\cdot\cdot (1+ x^n)}$

Published on 17 Apr 2026 - 4:25

score 60 · Answer 14 · 2026-04-11 22:32:54

60

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Is it possible to find the limit of this?

Published on 11 Apr 2026 - 22:32

score 540 · Answer 15 · 2026-04-12 00:40:51

540

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A Sum that came up while solving a integral

Published on 12 Apr 2026 - 0:40

List Question

Generating functions and central binomial coefficient

Prove that $1+2^1+2^2+\ldots +2^n=2^{n+1}-1$ using induction

How prove this identity$\sum_{k=0}^{n}\binom{2k}{k}\binom{n+k}{2k}(s-t)^{n-k}t^k=\sum_{k=0}^{n}\binom{n}{k}^2s^{n-k}t^k$

How to prove combinatorial identity $\sum_{k=0}^s{s\choose k}{m\choose k}{k\choose m-s}={2s\choose s}{s\choose m-s}$?

Product of sums equal to sum of products

Does $\sum_{n=1}^{\infty}\frac{\cos\left(\frac{n\pi}{2}\right)}{\sqrt{n}}$ converge?

Estimation of a sum independent of $n$

How to prove this Catalan number identity

Convolution of discrete uniform distributions

Is there a summation formula for this equation (contains square roots, and functions within the square root)?

Sum of segments inside a right triangle.

Prove that $\sum_{n=0}^\infty \frac{(-1)^n}{3n+1} = \frac{\pi}{3\sqrt{3}}+\frac{\log 2}{3}$

convergence of infinite series $\sum_{n=1}^\infty \frac{x^n}{(1+x)(1+x^2)(1+x^3)\cdot\cdot\cdot (1+ x^n)}$

Is it possible to find the limit of this?

A Sum that came up while solving a integral

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