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Can someone provide me the expansion for the following?

$$A=\left( \sum_{n=1}^N a_n \right)^4 $$

I found square and cubic expansions here

If there is any general expansion for power $k$

$$A=\left( \sum_{n=1}^N a_n \right)^k $$ Please provide too.

Frey
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1 Answers1

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This actually is related to multinomial theorem:

In your case we have: $$\left(\sum_{n=1}^{N}a_{n}\right)^{k}=\sum_{t_{1}+...+t_{N}=k}^{ }{{k}\choose{t_1,..,t_N}}\prod_{n=1}^{N}\left(a_{n}\right)^{t_{n}}$$