Sequences and Series/Infinite products

infinite product Let be a sequence of numbers in or . If the limit exists, it is called the infinite product of and denoted by . necessary condition for convergence of infinite products In order for the infinite product of a sequence to exist and not to be zero, it is necessary that . Suppose that not . Then there exists and an infinite sequence such that for all we have . Thus, upon denoting , we will have . Suppose for a contradiction that exited and was equal to . Then when is sufficiently large, we will have , which is a contradiction. series criterion for the convergence of infinite products Let be a sequence of real numbers. If , then converges.