List questions from binomial-coefficients

Published on 24 Aug 2014 - 22:07

346

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Appromixation of binomial coefficient for large numbers

Published on 25 Aug 2014 - 15:22

92

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How to evaluate $\sum_{k=0}^{n} \alpha^k \binom{n}{k}$?

Published on 28 Aug 2014 - 0:47

137

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Proof that $\dfrac{1}{e^x}=e^{-x}$ without converting it to $e^{x}e^{-x}=1$.

Published on 04 Apr 2026 - 5:19

615

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Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}\;$

Published on 26 Mar 2026 - 8:03

262

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Evaluation of $\sum_{k=0}^n{n\choose k}^2u^k$

Published on 29 Aug 2014 - 6:36

202

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Binomial Congruence (mod 5) Identity

Published on 31 Mar 2026 - 5:38

299

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How to evaluate the finite sum $\sum_{k=0}^n{\alpha \choose k}^2\lambda^k$

Published on 31 Aug 2014 - 8:54

68

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How prove this sum $\sum\limits_{n=k}^{\infty}\dbinom{n}{k}\left(\dfrac{-z}{1-z}\right)^n$

Published on 31 Aug 2014 - 15:11

4.2k

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How to solve 0.5 choose 4?

Published on 31 Aug 2014 - 19:37

90

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Number after binomial coefficient

Published on 02 Sep 2014 - 9:18

379

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Evaluate the sum $ \sum_{i=0}^{n} (-1)^{n-i} \binom{n}{i} f(i)$

Published on 30 Mar 2026 - 17:38

85

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Meaning of coefficients when multiplying together $(1+x^a)(1+x^b)(1+x^c)\cdots$?

Published on 28 Mar 2026 - 22:31

1.2k

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Generating functions to solve number of integer solution problem

Published on 30 Mar 2026 - 17:38

265

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How to prove the following limit: $\lim_{n \to +\infty} 4^n\left[\sum_{k=0}^n (-1)^k{n\choose k}\ln (n+k)\right]=0$?

Published on 05 Sep 2014 - 2:07

List Question

Sum of combinations of the n by consecutive k

Appromixation of binomial coefficient for large numbers

How to evaluate $\sum_{k=0}^{n} \alpha^k \binom{n}{k}$?

Proof that $\dfrac{1}{e^x}=e^{-x}$ without converting it to $e^{x}e^{-x}=1$.

Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}\;$

Evaluation of $\sum_{k=0}^n{n\choose k}^2u^k$

Binomial Congruence (mod 5) Identity

How to evaluate the finite sum $\sum_{k=0}^n{\alpha \choose k}^2\lambda^k$

How prove this sum $\sum\limits_{n=k}^{\infty}\dbinom{n}{k}\left(\dfrac{-z}{1-z}\right)^n$

How to solve 0.5 choose 4?

Number after binomial coefficient

Evaluate the sum $ \sum_{i=0}^{n} (-1)^{n-i} \binom{n}{i} f(i)$

Meaning of coefficients when multiplying together $(1+x^a)(1+x^b)(1+x^c)\cdots$?

Generating functions to solve number of integer solution problem

How to prove the following limit: $\lim_{n \to +\infty} 4^n\left[\sum_{k=0}^n (-1)^k{n\choose k}\ln (n+k)\right]=0$?

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