Question

coefficients of $x^k$ and $x^{k+1}$

score 71 · Answer 1 · 2026-04-14 05:36:50

71

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coefficients of $x^k$ and $x^{k+1}$

Published on 14 Apr 2026 - 5:36

score 303 · Answer 2 · 2026-04-17 07:56:54

303

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Simplification of $\binom{50}{0}\binom{50}{1}+\binom{50}{1}\binom{50}{2}+\cdots+\binom{50}{49}\binom{50}{50}$

Published on 17 Apr 2026 - 7:56

score 82 · Answer 3 · 2026-04-16 23:31:24

82

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Find the co-efficient of $x^{18}$ in the expansion of $(x+1)(x+2)...(x+10)(2x+1)(2x+3)...(2x+19)$.

Published on 16 Apr 2026 - 23:31

score 67 · Answer 4 · 2026-04-15 20:31:35

67

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Is there a formula for determining the coefficients of $\prod\limits_{i=0}^n(a+i)$

Published on 15 Apr 2026 - 20:31

score 62 · Answer 5 · 2026-04-16 15:46:43

Explain why twice the sum $\binom{12}{0} + \binom{12}{1} + \binom{12}{2} + \binom{12}{3} + \binom{12}{4} + \binom{12}{5}$ is $2^{12}-\binom{12}6$

score 778 · Answer 6 · 2026-04-10 18:50:07

778

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Pascals triangle pathways

Published on 10 Apr 2026 - 18:50

score 1.1k · Answer 7 · 2026-04-13 05:00:53

1.1k

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The nth power of a jordan block involving binomial coefficients

Published on 13 Apr 2026 - 5:00

score 443 · Answer 8 · 2026-04-14 23:26:00

443

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Prove $\sum_{k=0}^{58}\binom{2017+k}{58-k}\binom{2075-k}{k}=\sum_{k=0}^{29}\binom{4091-2k}{58-2k}$

Published on 14 Apr 2026 - 23:26

score 211 · Answer 9 · 2026-04-14 05:31:21

211

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Is there a quick way of finding the coefficients in an expression like $(ax^3+bx^2+cx+d)^3$?

Published on 14 Apr 2026 - 5:31

score 120 · Answer 10 · 2026-04-11 17:36:47

120

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induction regarding the binomial coefficient

Published on 11 Apr 2026 - 17:36

score 694 · Answer 11 · 2026-04-15 03:14:14

694

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Prove by Double Counting Method $\sum\limits_{k = 0}^m \binom{m}{k}\binom{n}{r + k} = \binom{m + n}{m + r}$

Published on 15 Apr 2026 - 3:14

score 169 · Answer 12 · 2026-04-16 18:55:21

169

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Proving $\sum \limits_{i=0}^k {n \choose i}(-1)^i = {n-1 \choose k}(-1)^k$

Published on 16 Apr 2026 - 18:55

score 74 · Answer 13 · 2026-04-13 23:30:47

74

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Combinatorics summation proof involving binomial coefficients

Published on 13 Apr 2026 - 23:30

score 51 · Answer 14 · 2026-04-17 08:38:55

51

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If I roll D copies of an S-sided dice, which is the probability that I will get at least M matches?

Published on 17 Apr 2026 - 8:38

score 202 · Answer 15 · 2026-04-16 15:41:02

202

Views

How to find the coefficients of the $k$-th term of $\left(\frac{x^n - 1}{x - 1}\right)^m$ for arbitrary $k$, $m$, and $n$?

Published on 16 Apr 2026 - 15:41

List Question

coefficients of $x^k$ and $x^{k+1}$

Simplification of $\binom{50}{0}\binom{50}{1}+\binom{50}{1}\binom{50}{2}+\cdots+\binom{50}{49}\binom{50}{50}$

Find the co-efficient of $x^{18}$ in the expansion of $(x+1)(x+2)...(x+10)(2x+1)(2x+3)...(2x+19)$.

Is there a formula for determining the coefficients of $\prod\limits_{i=0}^n(a+i)$

Explain why twice the sum $\binom{12}{0} + \binom{12}{1} + \binom{12}{2} + \binom{12}{3} + \binom{12}{4} + \binom{12}{5}$ is $2^{12}-\binom{12}6$

Pascals triangle pathways

The nth power of a jordan block involving binomial coefficients

Prove $\sum_{k=0}^{58}\binom{2017+k}{58-k}\binom{2075-k}{k}=\sum_{k=0}^{29}\binom{4091-2k}{58-2k}$

Is there a quick way of finding the coefficients in an expression like $(ax^3+bx^2+cx+d)^3$?

induction regarding the binomial coefficient

Prove by Double Counting Method $\sum\limits_{k = 0}^m \binom{m}{k}\binom{n}{r + k} = \binom{m + n}{m + r}$

Proving $\sum \limits_{i=0}^k {n \choose i}(-1)^i = {n-1 \choose k}(-1)^k$

Combinatorics summation proof involving binomial coefficients

If I roll D copies of an S-sided dice, which is the probability that I will get at least M matches?

How to find the coefficients of the $k$-th term of $\left(\frac{x^n - 1}{x - 1}\right)^m$ for arbitrary $k$, $m$, and $n$?

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