Infinite Product - Convergence Criteria

Convergence Criteria

The product of positive real numbers with a finite amount of

converges if and only if the sum

converges. This allows the translation of convergence criteria for infinite sums into convergence criteria for infinite products.

For products in which each, written as, for instance, where, the bounds

show that the infinite product converges precisely if the infinite sum of the pn converges. This relies on the Monotone convergence theorem.

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