- #1

dilan

- 71

- 0

I can understand the binomial, but I can't do the trinomial using the general sigma notation method.

Can someone please show me how to do this by using about 2 examples?

Thanks alot

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter dilan
- Start date

- #1

dilan

- 71

- 0

I can understand the binomial, but I can't do the trinomial using the general sigma notation method.

Can someone please show me how to do this by using about 2 examples?

Thanks alot

- #2

dilan

- 71

- 0

anyone can help me? :(

- #3

arildno

Science Advisor

Homework Helper

Gold Member

Dearly Missed

- 10,089

- 135

Let your numbers be a,b,c. Define d=b+c. Then, we have:

[tex](a+b+c)^{N}=(a+d)^{N}=\sum_{i=0}^{N}\binom{N}{i}a^{(N-i)}d^{i}=\sum_{i=0}^{N}\sum_{k=0}^{i}\binom{N}{i}\binom{i}{k}a^{(N-i)}b^{i-k}c^{k}[/tex]

Denote the powers of a,b,c as [itex]p_{a},p_{b},p_{c}[/itex], respectively.

We therefore have that N,i and k are given by:

[tex]k=p_{c},i=p_{b}+p_{c},N=p_{a}+p_{b}+p_{c}[/tex]

Thus, your coefficient, in terms of 3 powers are:

[tex]\binom{p_{a}+p_{b}+p_{c}}{p_{b}+p_{c}}\binom{p_{b}+p_{c}}{p_{c}}[/tex]

seeing this pattern should tell you how to find the coefficients for higher nomials.

[tex](a+b+c)^{N}=(a+d)^{N}=\sum_{i=0}^{N}\binom{N}{i}a^{(N-i)}d^{i}=\sum_{i=0}^{N}\sum_{k=0}^{i}\binom{N}{i}\binom{i}{k}a^{(N-i)}b^{i-k}c^{k}[/tex]

Denote the powers of a,b,c as [itex]p_{a},p_{b},p_{c}[/itex], respectively.

We therefore have that N,i and k are given by:

[tex]k=p_{c},i=p_{b}+p_{c},N=p_{a}+p_{b}+p_{c}[/tex]

Thus, your coefficient, in terms of 3 powers are:

[tex]\binom{p_{a}+p_{b}+p_{c}}{p_{b}+p_{c}}\binom{p_{b}+p_{c}}{p_{c}}[/tex]

seeing this pattern should tell you how to find the coefficients for higher nomials.

Last edited:

Share:

- Last Post

- Replies
- 0

- Views
- 580

- Last Post

- Replies
- 4

- Views
- 1K

- Last Post

- Replies
- 9

- Views
- 872

- Last Post

- Replies
- 1

- Views
- 740

- Last Post

- Replies
- 3

- Views
- 1K

- Replies
- 7

- Views
- 341

- Last Post

- Replies
- 2

- Views
- 804

- Last Post

- Replies
- 10

- Views
- 8K

MHB
4-adic expansion

- Last Post

- Replies
- 2

- Views
- 2K

- Last Post

- Replies
- 15

- Views
- 4K