Question

Are there identities on integers that be proved by checking finitely many cases?

score 65 · Answer 1 · 2026-04-03 15:18:42

65

Views

Are there identities on integers that be proved by checking finitely many cases?

Published on 03 Apr 2026 - 15:18

score 411 · Answer 2 · 2026-03-25 20:32:42

411

Views

Proof for a combinatorial identity

Published on 25 Mar 2026 - 20:32

score 50 · Answer 3 · 2026-03-28 13:27:18

50

Views

Proof appears to use substitution inconsistently.

Published on 28 Mar 2026 - 13:27

score 83 · Answer 4 · 2026-03-30 16:21:47

83

Views

Proving combinatorial identities

Published on 30 Mar 2026 - 16:21

score 92 · Answer 5 · 2020-07-17 17:15:39

92

Views

Sum of binomial coefficients multiplied by powers of two and something else

Published on 17 Jul 2020 - 17:15

score 412 · Answer 6 · 2026-03-27 13:42:08

412

Views

Is there a story proof behind the combinatorial identity $(n-2k)\binom{n}{k} = n\left[ \binom{n-1}{k} - \binom{n-1}{k-1} \right]$?

Published on 27 Mar 2026 - 13:42

score 113 · Answer 7 · 2020-07-17 20:57:00

113

Views

$ \sqrt[n]{ \binom{n}{1} \cdot \binom{n}{2} \cdot \binom{n}{2} ........... \binom{n}{n} }$

Published on 17 Jul 2020 - 20:57

score 137 · Answer 8 · 2026-03-26 01:34:55

137

Views

Coefficient of $x^n$ in $(x^2+3x+2)^n$

Published on 26 Mar 2026 - 1:34

score 101 · Answer 9 · 2020-07-18 10:39:34

101

Views

Showing $\sum_{\alpha=0}^k \binom{k+15}{\alpha + 10}\binom{k}{\alpha}=\frac{2^{2k+15}(k+6)(k+7)\left(\frac{2k+15}{2}\right)!}{\sqrtπ (k+10)!}$

Published on 18 Jul 2020 - 10:39

score 45 · Answer 10 · 2026-04-06 11:22:38

45

Views

Bound for deformed binomial coefficients

Published on 06 Apr 2026 - 11:22

score 64 · Answer 11 · 2020-07-18 21:21:37

64

Views

Approximation of $\frac {n-c \choose k} {n\choose k} $ using a radical

Published on 18 Jul 2020 - 21:21

score 145 · Answer 12 · 2020-07-18 23:28:36

145

Views

Evaluating a binomial summation

Published on 18 Jul 2020 - 23:28

score 68 · Answer 13 · 2020-07-19 06:15:50

68

Views

Solution to recurrence $c_{l+1,t}=c_{l,t+1}-c_{l-1,t+1}$.

Published on 19 Jul 2020 - 6:15

score 128 · Answer 14 · 2020-07-19 18:41:07

128

Views

Proving $\binom{2n}{n} \geq \frac{2^{2n}}{n+1}$

Published on 19 Jul 2020 - 18:41

score 39 · Answer 15 · 2020-07-19 19:41:57

39

Views

What is the approximation ratio between $n \choose k$ and $(n/k\cdot e)^k$

Published on 19 Jul 2020 - 19:41

List Question

Are there identities on integers that be proved by checking finitely many cases?

Proof for a combinatorial identity

Proof appears to use substitution inconsistently.

Proving combinatorial identities

Sum of binomial coefficients multiplied by powers of two and something else

Is there a story proof behind the combinatorial identity $(n-2k)\binom{n}{k} = n\left[ \binom{n-1}{k} - \binom{n-1}{k-1} \right]$?

$ \sqrt[n]{ \binom{n}{1} \cdot \binom{n}{2} \cdot \binom{n}{2} ........... \binom{n}{n} }$

Coefficient of $x^n$ in $(x^2+3x+2)^n$

Showing $\sum_{\alpha=0}^k \binom{k+15}{\alpha + 10}\binom{k}{\alpha}=\frac{2^{2k+15}(k+6)(k+7)\left(\frac{2k+15}{2}\right)!}{\sqrtπ (k+10)!}$

Bound for deformed binomial coefficients

Approximation of $\frac {n-c \choose k} {n\choose k} $ using a radical

Evaluating a binomial summation

Solution to recurrence $c_{l+1,t}=c_{l,t+1}-c_{l-1,t+1}$.

Proving $\binom{2n}{n} \geq \frac{2^{2n}}{n+1}$

What is the approximation ratio between $n \choose k$ and $(n/k\cdot e)^k$

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