Question

Prove combinatorially that $\sum_{i=1}^n {i(n-i+1)} = {n+2 \choose 3}$

score 96 · Answer 1 · 2018-03-30 10:55:25

96

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Prove combinatorially that $\sum_{i=1}^n {i(n-i+1)} = {n+2 \choose 3}$

Published on 30 Mar 2018 - 10:55

score 450 · Answer 2 · 2026-03-20 08:26:50

450

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Question in proving a recurrence relation for Catalan numbers

Published on 20 Mar 2026 - 8:26

score 46 · Answer 3 · 2026-03-17 07:31:55

46

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How to prove a property in the set partitions problem

Published on 17 Mar 2026 - 7:31

score 115 · Answer 4 · 2018-04-12 05:36:54

Comparing $\left({\frac{2^{10}}{11}}\right)^{11}$ and $\binom{10}1^2\cdot\binom{10}2^2\cdot\binom{10}3^2\cdot\binom{10}4^2\cdot\binom{10}5$

score 57 · Answer 5 · 2026-03-25 03:03:16

57

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How many people do we need for seemingly random meet up of each other?

Published on 25 Mar 2026 - 3:03

score 258 · Answer 6 · 2018-04-27 08:02:24

258

Views

Combinatorial or probabilistic proof of a binomial identity

Published on 27 Apr 2018 - 8:02

score 851 · Answer 7 · 2026-03-24 09:45:15

851

Views

Combinatorial and Algebraic Proof of an Identity involving Stirling Numbers of the second kind ${n+1\brace k+1}=\sum_i \binom{n}{i}{i\brace k}$

Published on 24 Mar 2026 - 9:45

score 158 · Answer 8 · 2026-03-25 12:26:05

158

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Zeta polynomial of the Boolean Lattice

Published on 25 Mar 2026 - 12:26

score 729 · Answer 9 · 2018-05-12 00:14:20

729

Views

British Maths Olympiad (BMO) 2003 Round 1 Question 4 what is wrong with this approach, can it be fixed?

Published on 12 May 2018 - 0:14

score 151 · Answer 10 · 2018-05-18 18:19:29

151

Views

Finding value of $\sum^{10}_{k=2}\binom{k}{2}\binom{12-k}{2}$

Published on 18 May 2018 - 18:19

score 344 · Answer 11 · 2026-03-24 18:06:57

344

Views

Combinatorial proof of $\sum_{k=0}^p {p \choose k}^2 {{n+2p-k}\choose {2p}} = {{n+p} \choose p}^2$

Published on 24 Mar 2026 - 18:06

score 678 · Answer 12 · 2026-03-23 18:32:55

678

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Sum of coefficients of even powers of x in $(1+x)^5 (1+x^2)^5$?

Published on 23 Mar 2026 - 18:32

score 112 · Answer 13 · 2018-06-05 20:16:27

112

Views

Interpret $\prod_{n=3}^\infty 1- \frac{1}{n\choose 2}$ as a probability

Published on 05 Jun 2018 - 20:16

score 308 · Answer 14 · 2018-06-06 22:34:10

308

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Spivak's Calculus: Proofs concerning Pascal's Triangle

Published on 06 Jun 2018 - 22:34

score 263 · Answer 15 · 2018-06-10 14:05:48

263

Views

Find a recurrence relation that gives a formula for the number of arrangements of wins and losses for aN (you stop playing at 3 losses in a row).

Published on 10 Jun 2018 - 14:05

List Question

Prove combinatorially that $\sum_{i=1}^n {i(n-i+1)} = {n+2 \choose 3}$

Question in proving a recurrence relation for Catalan numbers

How to prove a property in the set partitions problem

Comparing $\left({\frac{2^{10}}{11}}\right)^{11}$ and $\binom{10}1^2\cdot\binom{10}2^2\cdot\binom{10}3^2\cdot\binom{10}4^2\cdot\binom{10}5$

How many people do we need for seemingly random meet up of each other?

Combinatorial or probabilistic proof of a binomial identity

Combinatorial and Algebraic Proof of an Identity involving Stirling Numbers of the second kind ${n+1\brace k+1}=\sum_i \binom{n}{i}{i\brace k}$

Zeta polynomial of the Boolean Lattice

British Maths Olympiad (BMO) 2003 Round 1 Question 4 what is wrong with this approach, can it be fixed?

Finding value of $\sum^{10}_{k=2}\binom{k}{2}\binom{12-k}{2}$

Combinatorial proof of $\sum_{k=0}^p {p \choose k}^2 {{n+2p-k}\choose {2p}} = {{n+p} \choose p}^2$

Sum of coefficients of even powers of x in $(1+x)^5 (1+x^2)^5$?

Interpret $\prod_{n=3}^\infty 1- \frac{1}{n\choose 2}$ as a probability

Spivak's Calculus: Proofs concerning Pascal's Triangle

Find a recurrence relation that gives a formula for the number of arrangements of wins and losses for aN (you stop playing at 3 losses in a row).

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