- #1

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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

- Thread starter dilan
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- #1

- 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

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anyone can help me? :(

- #3

arildno

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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.

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