List questions from binomial-coefficients

Published on 25 Mar 2026 - 7:49

257

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Finite Binomial Sum

Published on 23 Mar 2026 - 20:51

909

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Simplify the expression - sum of squares of binomial coefficients

Published on 24 Mar 2026 - 7:25

138

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Get a (continuous) approximation for the equipotential lines of the function $ f(L,\Delta)=2^{-L}\binom{L}{\frac{L-\Delta}{2}}$

Published on 25 Mar 2026 - 1:18

100

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Is the sequence $a_{n}= {{n}\choose{[n/2]}}^{1/n}$ increasing?

Published on 25 Mar 2026 - 1:17

417

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How was the integral formula for the binomial coefficient discovered?

Published on 25 Mar 2026 - 5:46

841

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Binomial Coefficient deck of cards probability question

Published on 24 Mar 2026 - 1:36

175

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A sum of sum involving binomial coefficent.(my conjecture)

Published on 25 Mar 2026 - 5:41

273

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Binomial Harmonic Numbers

Published on 24 Mar 2026 - 23:41

38

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Comparing $\left[(\frac{u+1}{2n})^{2n} - (\frac{u}{2n})^{2n}\right]$ to $\left[(u+1)^n-u^n\right]$

Published on 24 Mar 2026 - 14:19

238

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extracting Catalan numbers from its generating function (binomial theorem)

Published on 20 Mar 2026 - 11:37

424

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Evaluating sum of binomial coefficients

Published on 23 Mar 2026 - 16:46

128

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Pascal’s triangle proof

Published on 24 Mar 2026 - 9:22

1.1k

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The sum $\sum_{r=0}^{20}r(20-r)\binom{20}{r}^2$

Published on 25 Mar 2026 - 7:53

389

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How to prove $\binom{-r}{k} = (-1)^k \binom{r + k - 1}{k}$?

Published on 24 Mar 2026 - 4:40

List Question

Constrained combinatorial question using generating functions

Finite Binomial Sum

Simplify the expression - sum of squares of binomial coefficients

Get a (continuous) approximation for the equipotential lines of the function $ f(L,\Delta)=2^{-L}\binom{L}{\frac{L-\Delta}{2}}$

Is the sequence $a_{n}= {{n}\choose{[n/2]}}^{1/n}$ increasing?

How was the integral formula for the binomial coefficient discovered?

Binomial Coefficient deck of cards probability question

A sum of sum involving binomial coefficent.(my conjecture)

Binomial Harmonic Numbers

Comparing $\left[(\frac{u+1}{2n})^{2n} - (\frac{u}{2n})^{2n}\right]$ to $\left[(u+1)^n-u^n\right]$

extracting Catalan numbers from its generating function (binomial theorem)

Evaluating sum of binomial coefficients

Pascal’s triangle proof

The sum $\sum_{r=0}^{20}r(20-r)\binom{20}{r}^2$

How to prove $\binom{-r}{k} = (-1)^k \binom{r + k - 1}{k}$?

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