Product operator

The product operator multiplies the terms of a sequence or partial sequence. It is denoted as

$\prod_{k=1}^n a_k=(a_1)(a_2)\cdots(a_{n-1})(a_n)$

Any infinite product of a_n will converge to a nonzero real number if and only if

$\sum_{n=1}^\infty\ln(a_n)=r$

converges. This can be determined by any convergence test.

A common application of the product operator is in factorials, where

$n!=\prod_{k=0}^{n-1}(n-k)=n(n-1)(n-2)\cdots(2)(1)$

See also

• Sequence
• Summation
• Series