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.
Read more about this topic: Infinite Product
Famous quotes containing the word criteria:
“The Hacker Ethic: Access to computers—and anything which might teach you something about the way the world works—should be unlimited and total.
Always yield to the Hands-On Imperative!
All information should be free.
Mistrust authority—promote decentralization.
Hackers should be judged by their hacking, not bogus criteria such as degrees, age, race, or position.
You can create art and beauty on a computer.
Computers can change your life for the better.”
—Steven Levy, U.S. writer. Hackers, ch. 2, “The Hacker Ethic,” pp. 27-33, Anchor Press, Doubleday (1984)