Question

Tighter upper bound on $x$ where $2^x \leq \sum_{i=0}^m{{x \choose i}\lambda^i}$

score 193 · Answer 1 · 2026-03-30 11:16:04

193

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Tighter upper bound on $x$ where $2^x \leq \sum_{i=0}^m{{x \choose i}\lambda^i}$

Published on 30 Mar 2026 - 11:16

score 62 · Answer 2 · 2026-03-27 07:17:11

62

Views

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

Published on 27 Mar 2026 - 7:17

score 45 · Answer 3 · 2026-03-27 02:39:47

45

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Fake Proof Regarding Factorization of Binomial Coefficients

Published on 27 Mar 2026 - 2:39

score 41 · Answer 4 · 2020-05-17 11:37:32

41

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Equality involving binomial coefficient in a integral

Published on 17 May 2020 - 11:37

score 124 · Answer 5 · 2020-05-17 16:28:34

124

Views

$\sum(-1)^{k}k^{2}C_{n}^{k}$

Published on 17 May 2020 - 16:28

score 81 · Answer 6 · 2026-03-27 07:11:43

81

Views

Combinatorics Proof 3kCk

Published on 27 Mar 2026 - 7:11

score 69 · Answer 7 · 2026-03-29 03:19:10

69

Views

Infinite sum power series

Published on 29 Mar 2026 - 3:19

score 55 · Answer 8 · 2026-04-01 07:17:19

55

Views

Where does this relation come from? $n^2-1 \approx (n-1)2$ for $n-1 \ll 1$

Published on 01 Apr 2026 - 7:17

score 370 · Answer 9 · 2020-05-18 12:47:01

370

Views

Partial sum of binomial coefficients n choose k multplied by k for k from n/2+1 to n

Published on 18 May 2020 - 12:47

score 150 · Answer 10 · 2026-03-27 10:31:22

150

Views

Given positive integers $n, k, i,$ prove $\binom{n}{k} = \sum_{j=i}^{n-k+i}\binom{j-i}{i-1}\binom{n-j}{k-i}$

Published on 27 Mar 2026 - 10:31

score 577 · Answer 11 · 2026-03-28 19:30:45

577

Views

After rolling two dice and flipping 12 coins. What is the probability that the # of heads is equal to the sum of the numbers showing on the two dice?

Published on 28 Mar 2026 - 19:30

score 1k · Answer 12 · 2026-03-27 10:31:26

1k

Views

Combinatorial explanation of ${n\choose r}={n-1\choose r-1}+{n-1\choose r}$

Published on 27 Mar 2026 - 10:31

score 125 · Answer 13 · 2026-03-28 07:53:36

125

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Given just a $4$-distinct-digit number. What are the odds that randomly chosen number has digit $1$ and digit $2$?

Published on 28 Mar 2026 - 7:53

score 78 · Answer 14 · 2026-03-25 11:20:19

78

Views

How to calculate the number of unsuited hands in Texas Hold'em opening hand

Published on 25 Mar 2026 - 11:20

score 77 · Answer 15 · 2020-05-20 19:08:34

77

Views

Middle binomial coefficient generator mod p

Published on 20 May 2020 - 19:08

List Question

Tighter upper bound on $x$ where $2^x \leq \sum_{i=0}^m{{x \choose i}\lambda^i}$

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

Fake Proof Regarding Factorization of Binomial Coefficients

Equality involving binomial coefficient in a integral

$\sum(-1)^{k}k^{2}C_{n}^{k}$

Combinatorics Proof 3kCk

Infinite sum power series

Where does this relation come from? $n^2-1 \approx (n-1)2$ for $n-1 \ll 1$

Partial sum of binomial coefficients n choose k multplied by k for k from n/2+1 to n

Given positive integers $n, k, i,$ prove $\binom{n}{k} = \sum_{j=i}^{n-k+i}\binom{j-i}{i-1}\binom{n-j}{k-i}$

After rolling two dice and flipping 12 coins. What is the probability that the # of heads is equal to the sum of the numbers showing on the two dice?

Combinatorial explanation of ${n\choose r}={n-1\choose r-1}+{n-1\choose r}$

Given just a $4$-distinct-digit number. What are the odds that randomly chosen number has digit $1$ and digit $2$?

How to calculate the number of unsuited hands in Texas Hold'em opening hand

Middle binomial coefficient generator mod p

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