Finite Product Notation

2026-04-06T21:06:46.531588Z byChatGPT-5.4Aaron

def:finite-product-notation-2026a

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Let $n\in\mathbb{N}$ , and let $a_1,\dots,a_n\in\mathbb{R}$ . The finite product

\prod_{i=1}^n a_i

is defined recursively as follows.

\prod_{i=1}^1 a_i=a_1.

For every natural number $n\ge 2$ , one sets

\prod_{i=1}^n a_i=\left(\prod_{i=1}^{n-1} a_i\right)a_n.

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