Infinite product

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...a_n 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.