Difference between revisions of "Infinite product"
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(New page: An '''infinite product''' :<math> \prod_{n=1}^{\infty} a_n = a_1 \; a_2 \; a_3 \cdots </math> of a sequence of numbers ''a''<sub>1</sub>, ''a''<sub>2</sub>, ''a''<sub>3</sub>, ... i...) |
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| − | of a [[sequence]] of numbers ''a''<sub>1</sub>, ''a''<sub>2</sub>, ''a''<sub>3</sub>, ... is defined to be the [[limit (mathematics)|limit]] of the partial products ''a''<sub>1</sub>''a''<sub>2</sub>...''a''<sub>''n''</sub> as ''n'' goes to infinity. The infinite product is said to ''[[convergence|converge]]'' when the limit exists and is not zero. Otherwise the product is said to | + | of a [[sequence]] of numbers ''a''<sub>1</sub>, ''a''<sub>2</sub>, ''a''<sub>3</sub>, ... is defined to be the [[limit (mathematics)|limit]] of the partial products ''a''<sub>1</sub>''a''<sub>2</sub>...''a''<sub>''n''</sub> as ''n'' goes to infinity. The infinite product is said to ''[[convergence|converge]]'' when the limit exists and is not zero. Otherwise the product is said to [[diverge]]. |
[[category:mathematics]] | [[category:mathematics]] | ||
Revision as of 16:37, April 10, 2007
An infinite product
- <math>
\prod_{n=1}^{\infty} a_n = a_1 \; a_2 \; a_3 \cdots </math>
of a sequence of numbers a1, a2, a3, ... is defined to be the limit of the partial products a1a2...an as n goes to infinity. The infinite product is said to converge when the limit exists and is not zero. Otherwise the product is said to diverge.