I have seen the expression the identity product in somewhere and I try to express it again as \begin{align} % \prod _{k=1}^K\left(1-x_{k}\right)=\sum _{k=1}^K \frac{(-1)^k}{k!}\underbrace{\sum _{n_1=1}^K \ldots \sum _{n_k=1}^K}_{n_1\neq n_2\neq \ldots \neq ~ n_k} \prod _{t=1}^k x_{n_t} % \end{align} However, I am not sure if it is correct expression or not ? Could you give me a hint ?
Is this correct for this expression?
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combinatorics
algebra-precalculus
1 Answers
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The good expression would be (don't forget $k=0$ !) $ \prod_{k=1}^K(1-x_k)=\sum_{k=0}^K(-1)^k\sum_{1\leq i_1<\ldots
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1Looks very spiffy to me, Student. – 2012-07-26