Question

$\sum_{k=1}^{n} \frac{k}{k !} \sum_{i=0}^{n-k} \frac{(-1)^{i}}{i !}=1$

score 75 · Answer 1 · 2020-05-01 21:55:34

75

Views

$\sum_{k=1}^{n} \frac{k}{k !} \sum_{i=0}^{n-k} \frac{(-1)^{i}}{i !}=1$

Published on 01 May 2020 - 21:55

score 307 · Answer 2 · 2026-03-26 01:11:57

307

Views

Connected path of diagonals across an $n\times n$ grid, and Lemma of Sperner

Published on 26 Mar 2026 - 1:11

score 182 · Answer 3 · 2020-05-02 19:23:02

182

Views

Help with this problem about a constructed number, that is from an arbitary n numbers, and that is divisible by a prime

Published on 02 May 2020 - 19:23

score 103 · Answer 4 · 2026-03-25 11:08:14

103

Views

Prove combinatorics equality?

Published on 25 Mar 2026 - 11:08

score 50 · Answer 5 · 2020-05-04 16:48:35

50

Views

combinatorial proof of $\sum_{k=1}^{n} k\binom{n}{k}^2 = n\binom{2n-1}{n-1} $

Published on 04 May 2020 - 16:48

score 425 · Answer 6 · 2020-05-06 09:27:59

425

Views

show this sum $\sum_{i=0}^{n}(-1)^{i-j}\binom{n+i}{i}\binom{n+k-i}{k-i}\binom{2n}{n+j-i}=\binom{2n}{n}$

Published on 06 May 2020 - 9:27

score 260 · Answer 7 · 2020-05-08 05:43:47

260

Views

Combinatorial proof of $\sum_{k=n}^{q-m} \binom{k}{n} \binom{q-k}{m} = \binom{q+1}{m+n+1}$

Published on 08 May 2020 - 5:43

score 46 · Answer 8 · 2020-05-10 16:01:34

46

Views

Combinatorial proof of $1+2(\sum_{i=0}^n 3^i)=3^{n+1}$

Published on 10 May 2020 - 16:01

score 91 · Answer 9 · 2026-03-27 04:17:02

91

Views

Use combinatorial reasoning to show that Stirling number

Published on 27 Mar 2026 - 4:17

score 27 · Answer 10 · 2020-05-14 09:18:18

27

Views

How to proceed with Vandermonde's formula when it's multipled with iterating variable?

Published on 14 May 2020 - 9:18

score 285 · Answer 11 · 2020-05-15 19:29:58

285

Views

Unexpected formulas for "exactly $k$ sets" and "at least $k$ sets" variations of the principle of inclusion-exclusion

Published on 15 May 2020 - 19:29

score 61 · Answer 12 · 2020-05-16 17:35:33

61

Views

Why does $\sum_{i=1}^{n-1} {n-1 \choose i} {m+1 \choose i+1} = \frac{(m+n)!}{m!n!}$

Published on 16 May 2020 - 17:35

score 200 · Answer 13 · 2020-05-17 11:08:03

200

Views

Double Counting(combinatorial proof) for $1^2\binom{n}{1} + 2^2\binom{n}{2}+3^2\binom{n}{3}+...+n^2\binom{n}{n}$ = $n(n+1)2^{n-2}$

Published on 17 May 2020 - 11:08

score 80 · Answer 14 · 2020-05-17 16:57:21

80

Views

Combinatorics Proof 3kCk

Published on 17 May 2020 - 16:57

score 396 · Answer 15 · 2026-03-26 11:08:11

396

Views

In how many different ways can we place $k$ elements in $n$ boxes in which each box has a fixed maximum capacity?

Published on 26 Mar 2026 - 11:08

List Question

$\sum_{k=1}^{n} \frac{k}{k !} \sum_{i=0}^{n-k} \frac{(-1)^{i}}{i !}=1$

Connected path of diagonals across an $n\times n$ grid, and Lemma of Sperner

Help with this problem about a constructed number, that is from an arbitary n numbers, and that is divisible by a prime

Prove combinatorics equality?

combinatorial proof of $\sum_{k=1}^{n} k\binom{n}{k}^2 = n\binom{2n-1}{n-1} $

show this sum $\sum_{i=0}^{n}(-1)^{i-j}\binom{n+i}{i}\binom{n+k-i}{k-i}\binom{2n}{n+j-i}=\binom{2n}{n}$

Combinatorial proof of $\sum_{k=n}^{q-m} \binom{k}{n} \binom{q-k}{m} = \binom{q+1}{m+n+1}$

Combinatorial proof of $1+2(\sum_{i=0}^n 3^i)=3^{n+1}$

Use combinatorial reasoning to show that Stirling number

How to proceed with Vandermonde's formula when it's multipled with iterating variable?

Unexpected formulas for "exactly $k$ sets" and "at least $k$ sets" variations of the principle of inclusion-exclusion

Why does $\sum_{i=1}^{n-1} {n-1 \choose i} {m+1 \choose i+1} = \frac{(m+n)!}{m!n!}$

Double Counting(combinatorial proof) for $1^2\binom{n}{1} + 2^2\binom{n}{2}+3^2\binom{n}{3}+...+n^2\binom{n}{n}$ = $n(n+1)2^{n-2}$

Combinatorics Proof 3kCk

In how many different ways can we place $k$ elements in $n$ boxes in which each box has a fixed maximum capacity?

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