Question

Show that $\binom {2n}n \leq(2n)^{\pi (2n)}$ where $\pi(2n) $ is number of prime number less than $2n$

score 202 · Answer 1 · 2018-07-08 12:25:52

202

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Show that $\binom {2n}n \leq(2n)^{\pi (2n)}$ where $\pi(2n) $ is number of prime number less than $2n$

Published on 08 Jul 2018 - 12:25

score 690 · Answer 2 · 2026-03-26 14:33:21

690

Views

Derivation of Binomial theorem

Published on 26 Mar 2026 - 14:33

score 123 · Answer 3 · 2018-07-10 16:15:36

123

Views

How to evaluate $\binom{n}{k}\bmod{m}$

Published on 10 Jul 2018 - 16:15

score 109 · Answer 4 · 2018-07-13 10:34:52

109

Views

About a specific step on a proof of ${p^Rm\choose p^R} \equiv m \pmod{mp}$

Published on 13 Jul 2018 - 10:34

score 241 · Answer 5 · 2026-03-25 06:10:54

241

Views

Can't prove this algebraically $\sum\limits_{i = 0}^n { n \choose i } \, !i = n! $

Published on 25 Mar 2026 - 6:10

score 60 · Answer 6 · 2018-07-15 00:23:38

60

Views

Hints for proving $\frac{1}{m^k} \binom{m}{k} < \frac{1}{n^k} \binom{n}{k}$

Published on 15 Jul 2018 - 0:23

score 480 · Answer 7 · 2026-03-26 14:32:01

480

Views

Proof that $\sum\limits _{n=1}^{\infty } n\sum\limits _{j=2}^{\infty }{\frac {(-1)^{j-1}}{j^2} \left( 1-{j}^{-1} \right)^{n-1}} = -\frac12$

Published on 26 Mar 2026 - 14:32

score 195 · Answer 8 · 2018-07-16 04:18:12

195

Views

Alternating sum of binomial coefficient times logarithm

Published on 16 Jul 2018 - 4:18

score 510 · Answer 9 · 2026-03-25 06:01:48

510

Views

$n$-element subsets of the set $\{1,2, ..., 2n\}$.

Published on 25 Mar 2026 - 6:01

score 35 · Answer 10 · 2018-07-16 14:20:45

35

Views

Formula for the coefficients of $m$th order the central difference scheme

Published on 16 Jul 2018 - 14:20

score 106 · Answer 11 · 2018-07-16 15:08:44

106

Views

Is there a simple formula for this polynomial sum?

Published on 16 Jul 2018 - 15:08

score 160 · Answer 12 · 2026-03-26 09:39:54

160

Views

Prove the identity with Stirling numbers.

Published on 26 Mar 2026 - 9:39

score 56 · Answer 13 · 2026-03-25 12:54:31

56

Views

Which monomials in $p$ and $q$ can be a probability in a finite coin experiment?

Published on 25 Mar 2026 - 12:54

score 426 · Answer 14 · 2018-07-18 04:26:32

426

Views

Sum of Squares of Binomial Coefficients Using Residue Theorem

Published on 18 Jul 2018 - 4:26

score 181 · Answer 15 · 2018-07-18 15:37:20

181

Views

a tough sum of binomial coefficients

Published on 18 Jul 2018 - 15:37

List Question

Show that $\binom {2n}n \leq(2n)^{\pi (2n)}$ where $\pi(2n) $ is number of prime number less than $2n$

Derivation of Binomial theorem

How to evaluate $\binom{n}{k}\bmod{m}$

About a specific step on a proof of ${p^Rm\choose p^R} \equiv m \pmod{mp}$

Can't prove this algebraically $\sum\limits_{i = 0}^n { n \choose i } \, !i = n! $

Hints for proving $\frac{1}{m^k} \binom{m}{k} < \frac{1}{n^k} \binom{n}{k}$

Proof that $\sum\limits _{n=1}^{\infty } n\sum\limits _{j=2}^{\infty }{\frac {(-1)^{j-1}}{j^2} \left( 1-{j}^{-1} \right)^{n-1}} = -\frac12$

Alternating sum of binomial coefficient times logarithm

$n$-element subsets of the set $\{1,2, ..., 2n\}$.

Formula for the coefficients of $m$th order the central difference scheme

Is there a simple formula for this polynomial sum?

Prove the identity with Stirling numbers.

Which monomials in $p$ and $q$ can be a probability in a finite coin experiment?

Sum of Squares of Binomial Coefficients Using Residue Theorem

a tough sum of binomial coefficients

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