Question

How many collected terms are in the expansion of $(x+y+z)^{10} (w+x+y+z)^2$?

score 355 · Answer 1 · 2026-03-26 19:39:40

355

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How many collected terms are in the expansion of $(x+y+z)^{10} (w+x+y+z)^2$?

Published on 26 Mar 2026 - 19:39

score 47 · Answer 2 · 2022-11-17 15:11:58

47

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Hi I am confused how to solve this question

Published on 17 Nov 2022 - 15:11

score 111 · Answer 3 · 2022-11-18 12:54:13

111

Views

Verify proof: $a^{n}-b^{n} = (a-b) \sum\limits_{k=0}^{n-1} a^{k}b^{n-1-k}$

Published on 18 Nov 2022 - 12:54

score 155 · Answer 4 · 2026-04-01 02:49:43

155

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How to prove the binomial identity $\binom{n + 1}{a + b + 1} = \sum_{k = 0}^n \binom{k}{a}\binom{n - k}{b}$

Published on 01 Apr 2026 - 2:49

score 69 · Answer 5 · 2022-11-29 02:06:19

69

Views

Factoring out a coefficient from binomial

Published on 29 Nov 2022 - 2:06

score 58 · Answer 6 · 2026-04-07 22:52:54

58

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Understanding the generalised binomial theorem

Published on 07 Apr 2026 - 22:52

score 1.6k · Answer 7 · 2022-12-02 13:13:49

1.6k

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Sum of coefficients in the expansion of $(2x+3y-2z)^n$.

Published on 02 Dec 2022 - 13:13

score 75 · Answer 8 · 2026-04-07 11:16:06

75

Views

How can I estimate the number of repeated selections

Published on 07 Apr 2026 - 11:16

score 62 · Answer 9 · 2022-12-14 17:54:20

62

Views

Show that all the zeros of $(az+1)^m-b (z+1)^m$ lie in $|z|<1,$ where $a>1$ and $|b|\leq 1.$

Published on 14 Dec 2022 - 17:54

score 123 · Answer 10 · 2022-12-25 23:10:09

123

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Assuming x is small, expand $\frac{\sqrt{1-x}}{\sqrt{1+2x}}$ up to and including the term in $x^{2}$

Published on 25 Dec 2022 - 23:10

score 68 · Answer 11 · 2022-12-29 17:22:44

68

Views

If $A=\lim_{n\to\infty}\bigg(\prod_{k=0}^{n} {n\choose k}\bigg) ^{\frac{1}{n(n+1)}}$. Then Find $A$

Published on 29 Dec 2022 - 17:22

score 36 · Answer 12 · 2023-01-02 13:39:46

36

Views

Trouble with understanding the proof of the contribution of the principle part on the coefficients of the function

Published on 02 Jan 2023 - 13:39

score 522 · Answer 13 · 2023-01-05 02:53:38

522

Views

Prove a binomial identity: $\sum_{i=1}^n i \binom{2n}{n-i}=\frac12(n+1) \binom{2n}{n-1}$

Published on 05 Jan 2023 - 2:53

score 76 · Answer 14 · 2023-01-06 07:24:14

76

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Solving $f\left( n \right) = \sum\limits_{i > j \ge 0} {{}^{n + 1}{C_i}{}^n{C_j}} $

Published on 06 Jan 2023 - 7:24

score 114 · Answer 15 · 2023-01-11 09:03:30

114

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Find the value of three expressions

Published on 11 Jan 2023 - 9:03

List Question

How many collected terms are in the expansion of $(x+y+z)^{10} (w+x+y+z)^2$?

Hi I am confused how to solve this question

Verify proof: $a^{n}-b^{n} = (a-b) \sum\limits_{k=0}^{n-1} a^{k}b^{n-1-k}$

How to prove the binomial identity $\binom{n + 1}{a + b + 1} = \sum_{k = 0}^n \binom{k}{a}\binom{n - k}{b}$

Factoring out a coefficient from binomial

Understanding the generalised binomial theorem

Sum of coefficients in the expansion of $(2x+3y-2z)^n$.

How can I estimate the number of repeated selections

Show that all the zeros of $(az+1)^m-b (z+1)^m$ lie in $|z|<1,$ where $a>1$ and $|b|\leq 1.$

Assuming x is small, expand $\frac{\sqrt{1-x}}{\sqrt{1+2x}}$ up to and including the term in $x^{2}$

If $A=\lim_{n\to\infty}\bigg(\prod_{k=0}^{n} {n\choose k}\bigg) ^{\frac{1}{n(n+1)}}$. Then Find $A$

Trouble with understanding the proof of the contribution of the principle part on the coefficients of the function

Prove a binomial identity: $\sum_{i=1}^n i \binom{2n}{n-i}=\frac12(n+1) \binom{2n}{n-1}$

Solving $f\left( n \right) = \sum\limits_{i > j \ge 0} {{}^{n + 1}{C_i}{}^n{C_j}} $

Find the value of three expressions

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