Absolute Convergence - Products of Series

Products of Series

The Cauchy product of two series converges to the product of the sums if at least one of the series converges absolutely. That is, suppose that

and .

The Cauchy product is defined as the sum of terms cn where:

Then, if either the an or bn sum converges absolutely, then

Read more about this topic:  Absolute Convergence

Famous quotes containing the words products of, products and/or series:

    It seemed there was a sort of poisoning, an auto-infection of the organisms, so Dr. Krokowski said; it was caused by the disintegration of a substance ... and the products of this disintegration operated like an intoxicant upon the nerve-centres of the spinal cord, with an effect similar to that of certain poisons, such as morphia, or cocaine.
    Thomas Mann (1875–1955)

    But, most of all, the Great Society is not a safe harbor, a resting place, a final objective, a finished work. It is a challenge constantly renewed, beckoning us toward a destiny where the meaning of our lives matches the marvelous products of our labor.
    Lyndon Baines Johnson (1908–1973)

    The theory of truth is a series of truisms.
    —J.L. (John Langshaw)