Question

Proof that the two sums are equal - the glass ball problem.

score 237 · Answer 1 · 2026-04-13 07:05:41

237

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Proof that the two sums are equal - the glass ball problem.

Published on 13 Apr 2026 - 7:05

score 107 · Answer 2 · 2026-04-10 16:36:24

107

Views

Generating function and binomial coefficients

Published on 10 Apr 2026 - 16:36

score 57 · Answer 3 · 2026-04-14 16:01:24

57

Views

Number of ways to select $t$ non adjacent couples of consecutive numbers.

Published on 14 Apr 2026 - 16:01

score 56 · Answer 4 · 2026-04-12 19:07:18

56

Views

A sum involving Bernoulli numbers and product of binomial coefficients

Published on 12 Apr 2026 - 19:07

score 166 · Answer 5 · 2026-04-15 01:34:33

166

Views

Finding sum of $\sum_{0\leq i<j\leq n} \binom{n}{i}$ and $\sum_{0\leq i<j\leq n}\binom{n}{j}$

Published on 15 Apr 2026 - 1:34

score 102 · Answer 6 · 2026-04-12 22:12:58

102

Views

Sum of square of terms in binomial expansion

Published on 12 Apr 2026 - 22:12

score 77 · Answer 7 · 2026-04-10 07:36:00

77

Views

Re-writing a sum of binomial coefficients as an integral of shifted Legendre polynomials

Published on 10 Apr 2026 - 7:36

score 71 · Answer 8 · 2026-04-11 19:17:06

71

Views

An infinite summation derived from the gambler's ruin problem

Published on 11 Apr 2026 - 19:17

score 62 · Answer 9 · 2026-04-13 19:59:21

62

Views

Evaluate $\lim_{n\to\infty}\sum_{r=0}^n\frac{n\choose r}{(r+4)n^r}$

Published on 13 Apr 2026 - 19:59

score 71 · Answer 10 · 2026-04-14 22:08:44

71

Views

$\lim_{n\to\infty}\left(\sum_{0\lt{i},j\lt{n}}{\binom{2i}{i}\binom{2j}{j}}\right)^\frac{1}{n}$

Published on 14 Apr 2026 - 22:08

score 154 · Answer 11 · 2026-04-17 03:48:46

154

Views

Evaluating a finite series

Published on 17 Apr 2026 - 3:48

score 84 · Answer 12 · 2026-04-09 01:03:27

84

Views

$n$ chips for 100 cookies problem — is there a counting solution?

Published on 09 Apr 2026 - 1:03

score 102 · Answer 13 · 2026-04-17 14:31:42

102

Views

Proof for $\sum_{k=0}^{n}\frac{(-1)^k}{k+1}\binom{n}{k}=\frac{1}{n+1}$ using induction.

Published on 17 Apr 2026 - 14:31

score 91 · Answer 14 · 2026-04-15 04:00:40

91

Views

Why $\sum _{k=0}^n (-1)^k {n \choose k} = 0$ doesn't hold when $n=0$, but the binomial theorem does?

Published on 15 Apr 2026 - 4:00

score 353 · Answer 15 · 2026-04-15 22:03:00

353

Views

Arbitrary decimal value of $A(n)=\left(\frac{11}{10}\right)^n$

Published on 15 Apr 2026 - 22:03

List Question

Proof that the two sums are equal - the glass ball problem.

Generating function and binomial coefficients

Number of ways to select $t$ non adjacent couples of consecutive numbers.

A sum involving Bernoulli numbers and product of binomial coefficients

Finding sum of $\sum_{0\leq i<j\leq n} \binom{n}{i}$ and $\sum_{0\leq i<j\leq n}\binom{n}{j}$

Sum of square of terms in binomial expansion

Re-writing a sum of binomial coefficients as an integral of shifted Legendre polynomials

An infinite summation derived from the gambler's ruin problem

Evaluate $\lim_{n\to\infty}\sum_{r=0}^n\frac{n\choose r}{(r+4)n^r}$

$\lim_{n\to\infty}\left(\sum_{0\lt{i},j\lt{n}}{\binom{2i}{i}\binom{2j}{j}}\right)^\frac{1}{n}$

Evaluating a finite series

$n$ chips for 100 cookies problem — is there a counting solution?

Proof for $\sum_{k=0}^{n}\frac{(-1)^k}{k+1}\binom{n}{k}=\frac{1}{n+1}$ using induction.

Why $\sum _{k=0}^n (-1)^k {n \choose k} = 0$ doesn't hold when $n=0$, but the binomial theorem does?

Arbitrary decimal value of $A(n)=\left(\frac{11}{10}\right)^n$

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