# Expansion of $(a_1 + a_2 + \cdots + a_k)^n$

Is there an expansion for the following summation? $$(a_1 + a_2 + \cdots + a_k)^n$$

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## 2 Answers

http://en.wikipedia.org/wiki/Multinomial_theorem

This is what you seek.

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It's a shame that the binomial theorem is almost never stated so that it is clearly a special case of the multinomial theorem: $$(x+y)^n = \sum_{p+q=n} \frac{n!}{p!q!} x^p y^q$$ –  lhf Oct 20 '10 at 11:02
I think if it's just a hyperlink then it should be a comment instead. –  anon Oct 20 '10 at 13:23
@muad: Not necessarily. This link perfectly answers the question at hand. See this meta thread. –  jericson Oct 20 '10 at 16:23
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Since you know what $(a+b)^{n}$ is you can take $A = a_{1} + a_{2} + \cdots + a_{k-1}$ and $B=a_{k}$ and try to simplify the big expression by the binomial theorem.

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But the resulting coefficient will be really big. –  user2468 Oct 20 '10 at 7:20
@M.S: Yes, i agree! –  anonymous Oct 20 '10 at 7:34
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