Question

Sum of binomial coefficients multiplied by terms of arithmetic series

score 141 · Answer 1 · 2026-04-06 17:13:38

141

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Sum of binomial coefficients multiplied by terms of arithmetic series

Published on 06 Apr 2026 - 17:13

score 400 · Answer 2 · 2026-03-30 11:14:06

400

Views

dividing binomial coefficient by a number

Published on 30 Mar 2026 - 11:14

score 127 · Answer 3 · 2026-03-30 14:40:20

127

Views

Calculating $\binom {2016}0 - \binom {2016}3 + \binom {2016}6 - \binom {2016}9 + ... +\binom {2016}{2016}$

Published on 30 Mar 2026 - 14:40

score 62 · Answer 4 · 2026-03-29 13:24:21

62

Views

For a fixed $k$ what is the value of $\sum_{l=1}^{5^m-1} \Big\lfloor \dfrac{l}{5^k}\Big \rfloor$

Published on 29 Mar 2026 - 13:24

score 253 · Answer 5 · 2026-03-26 01:11:06

253

Views

Evaluate hypergeometric $_6F_5\left(\{\frac12\}_6;1,\{\frac32\}_4;1\right)$

Published on 26 Mar 2026 - 1:11

score 50 · Answer 6 · 2026-03-27 12:02:02

50

Views

Missing piece for combinatorial proof

Published on 27 Mar 2026 - 12:02

score 330 · Answer 7 · 2026-03-28 12:31:22

330

Views

(At least 2) Binomial Distribution Question

Published on 28 Mar 2026 - 12:31

score 38 · Answer 8 · 2020-06-27 16:55:01

38

Views

To find the maximum of repeated balls extractions' probability

Published on 27 Jun 2020 - 16:55

score 199 · Answer 9 · 2026-03-25 19:04:33

199

Views

A summation similar to Vandermonde identity

Published on 25 Mar 2026 - 19:04

score 294 · Answer 10 · 2026-03-30 14:43:31

294

Views

Prove the inequality $\sum^m_{k=0} {n\choose k}\leq \left ( \frac{en}{m} \right)^m$

Published on 30 Mar 2026 - 14:43

score 271 · Answer 11 · 2026-03-31 11:33:55

271

Views

Closed form expression for $\sum\limits_{k=0}^{\infty}\frac{k4^k}{n+k}{n+k\choose n-k}{n\choose k}{2n\choose 2k}^{-1}$

Published on 31 Mar 2026 - 11:33

score 73 · Answer 12 · 2020-06-29 16:56:34

73

Views

Sum of squares of binomial coefficient with slight modification

Published on 29 Jun 2020 - 16:56

score 101 · Answer 13 · 2026-03-30 14:43:33

101

Views

Calculating $\binom{99}{0}+ \binom{100}{2}+ \binom{99}{3}+ \binom{100}{5}+ \binom{99}{6}+ \binom{100}{8}+ ..+ \binom{100}{98}+\binom{99}{99}$

Published on 30 Mar 2026 - 14:43

score 1.6k · Answer 14 · 2026-03-30 11:16:48

1.6k

Views

Simplifying ${n\choose k} - {n-1 \choose k}$.

Published on 30 Mar 2026 - 11:16

score 56 · Answer 15 · 2020-06-29 17:45:33

56

Views

If $a=7!$, $b=_{13}P_k$, $\frac{ab}{\operatorname{lcm}(a,b)}=120$, find the $k$

Published on 29 Jun 2020 - 17:45

List Question

Sum of binomial coefficients multiplied by terms of arithmetic series

dividing binomial coefficient by a number

Calculating $\binom {2016}0 - \binom {2016}3 + \binom {2016}6 - \binom {2016}9 + ... +\binom {2016}{2016}$

For a fixed $k$ what is the value of $\sum_{l=1}^{5^m-1} \Big\lfloor \dfrac{l}{5^k}\Big \rfloor$

Evaluate hypergeometric $_6F_5\left(\{\frac12\}_6;1,\{\frac32\}_4;1\right)$

Missing piece for combinatorial proof

(At least 2) Binomial Distribution Question

To find the maximum of repeated balls extractions' probability

A summation similar to Vandermonde identity

Prove the inequality $\sum^m_{k=0} {n\choose k}\leq \left ( \frac{en}{m} \right)^m$

Closed form expression for $\sum\limits_{k=0}^{\infty}\frac{k4^k}{n+k}{n+k\choose n-k}{n\choose k}{2n\choose 2k}^{-1}$

Sum of squares of binomial coefficient with slight modification

Calculating $\binom{99}{0}+ \binom{100}{2}+ \binom{99}{3}+ \binom{100}{5}+ \binom{99}{6}+ \binom{100}{8}+ ..+ \binom{100}{98}+\binom{99}{99}$

Simplifying ${n\choose k} - {n-1 \choose k}$.

If $a=7!$, $b=_{13}P_k$, $\frac{ab}{\operatorname{lcm}(a,b)}=120$, find the $k$

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