List questions from binomial-coefficients

Published on 05 Sep 2014 - 10:28

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Factorial as a sum. Insight appreciated

Published on 28 Mar 2026 - 5:21

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Using Binomial Theorem to prove the following

Published on 28 Mar 2026 - 17:05

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Why is $\sum\limits_{b=1}^{t-1} {t \choose b} 2^{t-b} = (3^t - 2^t - 1)$

Published on 07 Sep 2014 - 16:55

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Show that $\sum_{k=0}^{\infty} \binom{r}{k} \binom{s}{n+k} = \binom{r+s}{r+n}$.

Published on 07 Sep 2014 - 22:41

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Sums $\sum_{k = 0}^n k^t {n \choose k}$ where $t$ is a positive integer

Published on 08 Sep 2014 - 0:27

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Algorithm for determining whether certain numbers appear in Pascal's triangle

Published on 08 Sep 2014 - 14:12

190

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$\sum_{k+M = 0}^n {n \choose k} {n-k \choose m} = 3^n$ help with combinatorial reasoning

Published on 08 Sep 2014 - 23:34

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Consecutive terms in Pascal's Triangle

Published on 09 Sep 2014 - 13:42

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Proof of Pascal' identity

Published on 09 Sep 2014 - 15:07

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Evaluate $ \sum\limits_{j \in \mathbb{Z}_{\geq 0}} {n \choose r+kj}$ where $n,k$ are fixed

Published on 09 Sep 2014 - 20:44

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Challenge: How to prove this identity between bi- and trinomial coefficients?

Published on 25 Mar 2026 - 12:53

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Find $a_1$ given that $(1+x)^{100} = \sum_{i=0}^{100} a_ix^i$

Published on 10 Sep 2014 - 23:12

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find $\sum_{k=0}^{t}(-1)^k\binom{t}{k}^2$ for odd t then for even t

Published on 10 Sep 2014 - 23:49

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Finding the coefficient of $x^{46}$ in an expression

Published on 11 Sep 2014 - 15:30

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Find coefficient of $x^3$ in (2+x) ^(3/2)/(1-x)

Factorial as a sum. Insight appreciated

Using Binomial Theorem to prove the following

Why is $\sum\limits_{b=1}^{t-1} {t \choose b} 2^{t-b} = (3^t - 2^t - 1)$

Show that $\sum_{k=0}^{\infty} \binom{r}{k} \binom{s}{n+k} = \binom{r+s}{r+n}$.

Sums $\sum_{k = 0}^n k^t {n \choose k}$ where $t$ is a positive integer

Algorithm for determining whether certain numbers appear in Pascal's triangle

$\sum_{k+M = 0}^n {n \choose k} {n-k \choose m} = 3^n$ help with combinatorial reasoning

Consecutive terms in Pascal's Triangle

Proof of Pascal' identity

Evaluate $ \sum\limits_{j \in \mathbb{Z}_{\geq 0}} {n \choose r+kj}$ where $n,k$ are fixed

Challenge: How to prove this identity between bi- and trinomial coefficients?

Find $a_1$ given that $(1+x)^{100} = \sum_{i=0}^{100} a_ix^i$

find $\sum_{k=0}^{t}(-1)^k\binom{t}{k}^2$ for odd t then for even t

Finding the coefficient of $x^{46}$ in an expression

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