Question

The status of the sum: $\sum_{k=m}^{n} \frac{{k \choose m}}{k+1}$

score 71 · Answer 1 · 2026-03-29 10:08:56

71

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The status of the sum: $\sum_{k=m}^{n} \frac{{k \choose m}}{k+1}$

Published on 29 Mar 2026 - 10:08

score 62 · Answer 2 · 2019-10-03 16:46:19

62

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asymptotic for sums of binomials

Published on 03 Oct 2019 - 16:46

score 70 · Answer 3 · 2026-03-29 10:18:10

70

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What is the sum of the given series?

Published on 29 Mar 2026 - 10:18

score 330 · Answer 4 · 2026-03-25 17:40:15

330

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Expanding a product of linear combinations with coefficients $1$ and $-1$

Published on 25 Mar 2026 - 17:40

score 123 · Answer 5 · 2019-10-04 16:37:45

123

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How do I prove $\sum_{k=0}^{n}\binom{n}{k}\cdot 2^k = 3^n$?

Published on 04 Oct 2019 - 16:37

score 16 · Answer 6 · 2026-03-11 00:10:39

16

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Relation between number of possible arrangements of $x's$ and $y's$ and the coefficient of the $(r+1)^{th}$ term

Published on 11 Mar 2026 - 0:10

score 291 · Answer 7 · 2019-10-06 08:19:36

291

Views

find the coefficient of $x^{25}$

Published on 06 Oct 2019 - 8:19

score 173 · Answer 8 · 2026-03-29 11:50:06

173

Views

Is it true that $\lim_{m\to\infty} \sum_{k=0}^{\frac{m-1}{2}} {m\choose{k}}(a^{k+1}(1-a)^{m-k}+a^k(1-a)^{m-k+1})=\min(a,1-a)$?

Published on 29 Mar 2026 - 11:50

score 187 · Answer 9 · 2019-10-06 23:21:55

187

Views

Identity of Binomial sum

Published on 06 Oct 2019 - 23:21

score 279 · Answer 10 · 2026-03-29 11:49:59

279

Views

Find the coefficient of $ x^6 $in the given expansion.

Published on 29 Mar 2026 - 11:49

score 208 · Answer 11 · 2019-10-08 16:08:05

208

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I cannot prove that $ \sum_{k=0}^n \sum_{i=k}^n {n \choose k} {n+1 \choose i+1} = 2^{2n} $

Published on 08 Oct 2019 - 16:08

score 220 · Answer 12 · 2019-10-08 17:25:33

220

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Proof by induction for ${m+n \choose n+r} = \sum\limits_{k=0}^{m}{m \choose k}{n \choose r+k}$

Published on 08 Oct 2019 - 17:25

score 3k · Answer 13 · 2026-03-29 11:44:22

3k

Views

How many permutations of $ABCDEFG$ contain $AB$ and $DC$?

Published on 29 Mar 2026 - 11:44

score 500 · Answer 14 · 2026-03-30 05:26:53

500

Views

Prove that $\int \binom{n}{k}p^k(1−p)^{n−k}\,dp$ from $0$ to $1$ is $\frac{1}{n+1}$

Published on 30 Mar 2026 - 5:26

score 326 · Answer 15 · 2019-10-12 20:53:25

326

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How many pairs of students (with one working alone) are possible if there are $21$ students in a class?

Published on 12 Oct 2019 - 20:53

List Question

The status of the sum: $\sum_{k=m}^{n} \frac{{k \choose m}}{k+1}$

asymptotic for sums of binomials

What is the sum of the given series?

Expanding a product of linear combinations with coefficients $1$ and $-1$

How do I prove $\sum_{k=0}^{n}\binom{n}{k}\cdot 2^k = 3^n$?

Relation between number of possible arrangements of $x's$ and $y's$ and the coefficient of the $(r+1)^{th}$ term

find the coefficient of $x^{25}$

Is it true that $\lim_{m\to\infty} \sum_{k=0}^{\frac{m-1}{2}} {m\choose{k}}(a^{k+1}(1-a)^{m-k}+a^k(1-a)^{m-k+1})=\min(a,1-a)$?

Identity of Binomial sum

Find the coefficient of $ x^6 $in the given expansion.

I cannot prove that $ \sum_{k=0}^n \sum_{i=k}^n {n \choose k} {n+1 \choose i+1} = 2^{2n} $

Proof by induction for ${m+n \choose n+r} = \sum\limits_{k=0}^{m}{m \choose k}{n \choose r+k}$

How many permutations of $ABCDEFG$ contain $AB$ and $DC$?

Prove that $\int \binom{n}{k}p^k(1−p)^{n−k}\,dp$ from $0$ to $1$ is $\frac{1}{n+1}$

How many pairs of students (with one working alone) are possible if there are $21$ students in a class?

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