List questions from binomial-coefficients

Published on 31 Mar 2026 - 16:52

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Finding the combination of creating 2 pairs

Published on 12 Apr 2026 - 10:47

354

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Inverse Binomial Coefficient Lookup/Check

Published on 16 Nov 2016 - 16:34

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Simplifying Binomial coefficients within summations

Published on 10 Apr 2026 - 18:00

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Proving $\sum_\limits{k=0}^n \binom {k+m} {k} = \binom {m+n+1} {n}$ by induction.

Published on 16 Nov 2016 - 20:19

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How to prove that $n \choose r$ = $\frac{n+1-r}{r}$ $n \choose r-1$ without using the factorial expansion of $n \choose r$?

Published on 11 Apr 2026 - 22:13

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What is the value of $0 \choose 0$?

Published on 19 Nov 2016 - 5:03

480

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binomial sum approximation

Published on 12 Apr 2026 - 17:44

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How can I derive what is $1\cdot 2\cdot 3\cdot 4 + 2\cdot 3\cdot 4\cdot 5+ 3\cdot 4\cdot 5\cdot 6+\cdots + (n-3)(n-2)(n-1)(n)$ ??

Published on 19 Nov 2016 - 13:13

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How to find $\sum_{n=1}^{\infty}{\binom{2n-1}{n} x^n}, |x| < \frac{1}{4} ?$

Published on 19 Nov 2016 - 17:40

630

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Combinatorial proof of the identity $3^n=\sum_{k=0}^n \binom nk 2^k$

Published on 11 Apr 2026 - 16:28

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How to show $\sum_{n=1}^{a+b} \frac{(-1)^n}{n}\binom{n}{n-a,n-b,a+b-n}=0$

Published on 20 Nov 2016 - 3:47

80

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Show that $ \sum_{k=0}^\infty \binom{\alpha}{k}x^k$, $|x| \leq 1 $ converges

Published on 20 Nov 2016 - 23:03

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The product of combinations, and how fast it grows

Published on 31 Mar 2026 - 4:50

90

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Sum of Lacunary Series of Binomial Coefficients with Rising Upper Parameter

Published on 21 Nov 2016 - 18:29

List Question

Harmonic series and the binomial theorem

Finding the combination of creating 2 pairs

Inverse Binomial Coefficient Lookup/Check

Simplifying Binomial coefficients within summations

Proving $\sum_\limits{k=0}^n \binom {k+m} {k} = \binom {m+n+1} {n}$ by induction.

How to prove that $n \choose r$ = $\frac{n+1-r}{r}$ $n \choose r-1$ without using the factorial expansion of $n \choose r$?

What is the value of $0 \choose 0$?

binomial sum approximation

How can I derive what is $1\cdot 2\cdot 3\cdot 4 + 2\cdot 3\cdot 4\cdot 5+ 3\cdot 4\cdot 5\cdot 6+\cdots + (n-3)(n-2)(n-1)(n)$ ??

How to find $\sum_{n=1}^{\infty}{\binom{2n-1}{n} x^n}, |x| < \frac{1}{4} ?$

Combinatorial proof of the identity $3^n=\sum_{k=0}^n \binom nk 2^k$

How to show $\sum_{n=1}^{a+b} \frac{(-1)^n}{n}\binom{n}{n-a,n-b,a+b-n}=0$

Show that $ \sum_{k=0}^\infty \binom{\alpha}{k}x^k$, $|x| \leq 1 $ converges

The product of combinations, and how fast it grows

Sum of Lacunary Series of Binomial Coefficients with Rising Upper Parameter

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