Question

Binomial coefficient identity with alternating summands

score 51 · Answer 1 · 2024-01-25 23:13:37

51

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Binomial coefficient identity with alternating summands

Published on 25 Jan 2024 - 23:13

score 68 · Answer 2 · 2024-02-01 00:35:43

68

Views

Confusion regarding the nth term in a binomial expansion (positive integral index)

Published on 01 Feb 2024 - 0:35

score 49 · Answer 3 · 2024-02-01 22:17:22

49

Views

Can we solve this only by using bijection?

Published on 01 Feb 2024 - 22:17

score 26 · Answer 4 · 2024-02-03 20:22:25

26

Views

binomial approximation doubt

Published on 03 Feb 2024 - 20:22

score 63 · Answer 5 · 2024-02-07 19:06:28

63

Views

How many $n$-digit numbers are there with no or even number of $1$s in them if only digits $1$, $2$, $3$ and $4$ are allowed?

Published on 07 Feb 2024 - 19:06

score 37 · Answer 6 · 2024-02-11 22:05:01

37

Views

Prove $(k+1)\binom{n}{k+1}+k\binom{n}{k}=n\binom{n}{k}$ for integers $0\le k\le n$

Published on 11 Feb 2024 - 22:05

score 130 · Answer 7 · 2024-02-15 11:59:09

130

Views

Evaluate the sum $\sum_{k=0}^n \frac{\binom n k}{(k+1)(k+3)} $

Published on 15 Feb 2024 - 11:59

score 51 · Answer 8 · 2024-02-16 10:46:32

51

Views

Absolute Value Condition in Generalized Binomial Theorem

Published on 16 Feb 2024 - 10:46

score 239 · Answer 9 · 2024-02-18 09:59:12

239

Views

Another Sophomore's Dream: $\int_{-\infty}^{\infty}\binom{n}{x}dx=\sum_{i=0}^{n} \binom{n}{i}$

Published on 18 Feb 2024 - 9:59

score 52 · Answer 10 · 2024-02-22 04:07:08

52

Views

In $\sum_{n=1}^{\left\lfloor \delta/2 \right\rfloor}$, what does ${\left\lfloor \delta/2 \right\rfloor}$ mean?

Published on 22 Feb 2024 - 4:07

score 99 · Answer 11 · 2024-02-23 04:04:47

99

Views

Proving $\sum_{i=0}^n (-1)^i\binom{n}{i}\binom{m+i}{m}=(-1)^n\binom{m}{m-n}$

Published on 23 Feb 2024 - 4:04

score 61 · Answer 12 · 2024-02-24 07:23:54

61

Views

Is Wikipedia's inductive proof of the Binomial Theorem acceptable?

Published on 24 Feb 2024 - 7:23

score 21 · Answer 13 · 2024-02-26 01:02:07

21

Views

Sum of products from $k=1$ to $m$ ( Context: Burton's proof of the binomial theorem)

Published on 26 Feb 2024 - 1:02

score 76 · Answer 14 · 2024-02-26 07:30:02

76

Views

Evaluating a binomial sum with a probabilistic interpretation

Published on 26 Feb 2024 - 7:30

score 61 · Answer 15 · 2024-02-26 22:39:32

61

Views

high order derivative of product

Published on 26 Feb 2024 - 22:39

List Question

Binomial coefficient identity with alternating summands

Confusion regarding the nth term in a binomial expansion (positive integral index)

Can we solve this only by using bijection?

binomial approximation doubt

How many $n$-digit numbers are there with no or even number of $1$s in them if only digits $1$, $2$, $3$ and $4$ are allowed?

Prove $(k+1)\binom{n}{k+1}+k\binom{n}{k}=n\binom{n}{k}$ for integers $0\le k\le n$

Evaluate the sum $\sum_{k=0}^n \frac{\binom n k}{(k+1)(k+3)} $

Absolute Value Condition in Generalized Binomial Theorem

Another Sophomore's Dream: $\int_{-\infty}^{\infty}\binom{n}{x}dx=\sum_{i=0}^{n} \binom{n}{i}$

In $\sum_{n=1}^{\left\lfloor \delta/2 \right\rfloor}$, what does ${\left\lfloor \delta/2 \right\rfloor}$ mean?

Proving $\sum_{i=0}^n (-1)^i\binom{n}{i}\binom{m+i}{m}=(-1)^n\binom{m}{m-n}$

Is Wikipedia's inductive proof of the Binomial Theorem acceptable?

Sum of products from $k=1$ to $m$ ( Context: Burton's proof of the binomial theorem)

Evaluating a binomial sum with a probabilistic interpretation

high order derivative of product

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