Question

Value of $\displaystyle \frac{p}{q}$ in binomial expression.

score 460 · Answer 1 · 2026-04-13 19:17:01

460

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Value of $\displaystyle \frac{p}{q}$ in binomial expression.

Published on 13 Apr 2026 - 19:17

score 63 · Answer 2 · 2026-04-13 23:22:51

63

Views

Use of Integration in proving the given relation with $\displaystyle \sum_{n=1}^{2022}$ $\frac{(-1)^{r-1}}{r}$ $\binom{2022}{r}$ as given;

Published on 13 Apr 2026 - 23:22

score 140 · Answer 3 · 2026-04-16 19:10:12

140

Views

Find sum $S = {n \choose 1} - 2 {n \choose 2} + 3{n \choose 3} - 4{n \choose 4} + \cdots + (-1)^{n} n {n \choose n}$

Published on 16 Apr 2026 - 19:10

score 28 · Answer 4 · 2026-04-14 15:29:18

28

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Is the expectation of ratio of elements in subset equal to the ratio of elements in the original set?

Published on 14 Apr 2026 - 15:29

score 328 · Answer 5 · 2026-04-13 13:21:37

328

Views

Binomial Expansions having a nonzero constant term.

Published on 13 Apr 2026 - 13:21

score 75 · Answer 6 · 2026-04-16 13:17:24

75

Views

Prove that ${n\choose0} + {n\choose3} + {n\choose6} + …. + {n\choose3k} \le \frac {1}{3} (2^n + 2)$

Published on 16 Apr 2026 - 13:17

score 119 · Answer 7 · 2026-04-17 07:26:28

119

Views

$1\binom{20}1+2\binom{20}2+3\binom{20}3+\dots+19\binom{20}{19}+20\binom{20}{20}$

Published on 17 Apr 2026 - 7:26

score 53 · Answer 8 · 2026-04-17 02:52:31

53

Views

Restricted sum of product of binomial coefficients

Published on 17 Apr 2026 - 2:52

score 55 · Answer 9 · 2026-04-15 23:38:46

55

Views

Closed expression for a $\sum\limits_{i=1}^{m} \binom{n+i}{n}$

Published on 15 Apr 2026 - 23:38

score 21 · Answer 10 · 2026-04-12 23:56:14

21

Views

what is the reciprocal inner product of lower triangle Pascal matrix?

Published on 12 Apr 2026 - 23:56

score 72 · Answer 11 · 2026-04-17 12:43:26

72

Views

Why does ${}^4 C_2 \times {}^8 C_3$ not give the number of $5$ member committees (with at least $2$ women) from $4$ women and $6$ men?

Published on 17 Apr 2026 - 12:43

score 124 · Answer 12 · 2026-03-26 19:19:01

124

Views

Given $m$ objects of type A and $n$ objects of type B, arrange them such that there are not more than two consecutive objects of type B.

Published on 26 Mar 2026 - 19:19

score 52 · Answer 13 · 2026-04-10 13:41:51

52

Views

Simplify and Prove the identity $\sum_{j=k}^n \binom jk = \binom{n + 1}{k + 1}$

Published on 10 Apr 2026 - 13:41

score 61 · Answer 14 · 2026-04-13 06:06:45

61

Views

Summation of products of every third term in two different binomial series?

Published on 13 Apr 2026 - 6:06

score 368 · Answer 15 · 2026-04-17 09:36:30

Calculating $\sum\limits_{k=0}^n\binom{n}{k}p^k(1-p)^{n-k}\frac{(\frac{p}{q})^k(\frac{1-p}{1-q})^{n-k}}{1+(\frac{p}{q})^k(\frac{1-p}{1-q})^{n-k}}$

List Question

Value of $\displaystyle \frac{p}{q}$ in binomial expression.

Use of Integration in proving the given relation with $\displaystyle \sum_{n=1}^{2022}$ $\frac{(-1)^{r-1}}{r}$ $\binom{2022}{r}$ as given;

Find sum $S = {n \choose 1} - 2 {n \choose 2} + 3{n \choose 3} - 4{n \choose 4} + \cdots + (-1)^{n} n {n \choose n}$

Is the expectation of ratio of elements in subset equal to the ratio of elements in the original set?

Binomial Expansions having a nonzero constant term.

Prove that ${n\choose0} + {n\choose3} + {n\choose6} + …. + {n\choose3k} \le \frac {1}{3} (2^n + 2)$

$1\binom{20}1+2\binom{20}2+3\binom{20}3+\dots+19\binom{20}{19}+20\binom{20}{20}$

Restricted sum of product of binomial coefficients

Closed expression for a $\sum\limits_{i=1}^{m} \binom{n+i}{n}$

what is the reciprocal inner product of lower triangle Pascal matrix?

Why does ${}^4 C_2 \times {}^8 C_3$ not give the number of $5$ member committees (with at least $2$ women) from $4$ women and $6$ men?

Given $m$ objects of type A and $n$ objects of type B, arrange them such that there are not more than two consecutive objects of type B.

Simplify and Prove the identity $\sum_{j=k}^n \binom jk = \binom{n + 1}{k + 1}$

Summation of products of every third term in two different binomial series?

Calculating $\sum\limits_{k=0}^n\binom{n}{k}p^k(1-p)^{n-k}\frac{(\frac{p}{q})^k(\frac{1-p}{1-q})^{n-k}}{1+(\frac{p}{q})^k(\frac{1-p}{1-q})^{n-k}}$

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