Question

Non-inductive, not combinatorial proof of $\sum_{i \mathop = 0}^n \binom n i^2 = \binom {2 n} n$

score 905 · Answer 1 · 2026-04-03 08:48:27

905

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Non-inductive, not combinatorial proof of $\sum_{i \mathop = 0}^n \binom n i^2 = \binom {2 n} n$

Published on 03 Apr 2026 - 8:48

score 197 · Answer 2 · 2026-04-12 18:26:09

197

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Solve sum with n and i

Published on 12 Apr 2026 - 18:26

score 258 · Answer 3 · 2014-05-13 20:24:18

258

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Generating: $\frac{1}{2\ln2}-\frac{1}{3\ln3}+\frac{1}{4\ln4}...$

Published on 13 May 2014 - 20:24

score 285 · Answer 4 · 2026-04-03 08:48:37

285

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How can I find $\sum\limits_{n=i+1}^\infty \binom{n-1}{i}\left (\frac{1}{3}\right)^{n}$?

Published on 03 Apr 2026 - 8:48

score 892 · Answer 5 · 2026-04-06 20:28:23

892

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Summation Notation Confusion

Published on 06 Apr 2026 - 20:28

score 72 · Answer 6 · 2026-04-12 08:15:27

72

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Summation : Series with each term having components of two different series

Published on 12 Apr 2026 - 8:15

score 75 · Answer 7 · 2026-04-13 02:31:05

75

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Is there a formula for $f(n)=\sum_{k=2}^{n}\frac{1}{\sin^{2}(\frac{\pi }{k})}$

Published on 13 Apr 2026 - 2:31

score 1.4k · Answer 8 · 2026-03-26 16:23:11

1.4k

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Finding the n-th partial sum of an arithmetic progression

Published on 26 Mar 2026 - 16:23

score 1.3k · Answer 9 · 2014-05-15 04:49:53

1.3k

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Summation with absolute value $\sum_{k=-2}^{\infty}(\frac{1}{2})^{k}\alpha^{|n-k|}$

Published on 15 May 2014 - 4:49

score 686 · Answer 10 · 2026-04-09 17:36:55

686

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A question on a sum of $q$-binomial coefficients

Published on 09 Apr 2026 - 17:36

score 899 · Answer 11 · 2026-04-09 05:30:44

899

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Double sum trouble

Published on 09 Apr 2026 - 5:30

score 153 · Answer 12 · 2026-04-09 12:46:26

153

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How to find sum of factors of $2^{2012}$?

Published on 09 Apr 2026 - 12:46

score 109 · Answer 13 · 2026-04-03 10:44:50

109

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Evaluate the sum $\sum_{0\leq j < k\leq n}\binom{n}{j}\binom{n}{k}$

Published on 03 Apr 2026 - 10:44

score 321 · Answer 14 · 2026-04-10 12:09:37

321

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How to sum this infinite series

Published on 10 Apr 2026 - 12:09

score 379 · Answer 15 · 2026-04-03 10:38:59

379

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Proving $\sum_{k=1}^{n}\binom{n-1}{k-1}{\binom{n+k}{k}}^{-1}=\frac 12$ combinatorially

Published on 03 Apr 2026 - 10:38

List Question

Non-inductive, not combinatorial proof of $\sum_{i \mathop = 0}^n \binom n i^2 = \binom {2 n} n$

Solve sum with n and i

Generating: $\frac{1}{2\ln2}-\frac{1}{3\ln3}+\frac{1}{4\ln4}...$

How can I find $\sum\limits_{n=i+1}^\infty \binom{n-1}{i}\left (\frac{1}{3}\right)^{n}$?

Summation Notation Confusion

Summation : Series with each term having components of two different series

Is there a formula for $f(n)=\sum_{k=2}^{n}\frac{1}{\sin^{2}(\frac{\pi }{k})}$

Finding the n-th partial sum of an arithmetic progression

Summation with absolute value $\sum_{k=-2}^{\infty}(\frac{1}{2})^{k}\alpha^{|n-k|}$

A question on a sum of $q$-binomial coefficients

Double sum trouble

How to find sum of factors of $2^{2012}$?

Evaluate the sum $\sum_{0\leq j < k\leq n}\binom{n}{j}\binom{n}{k}$

How to sum this infinite series

Proving $\sum_{k=1}^{n}\binom{n-1}{k-1}{\binom{n+k}{k}}^{-1}=\frac 12$ combinatorially

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