Absolute Convergence

Absolute Convergence

In mathematics, an infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute value of the summand is finite. More precisely, a real or complex series is said to converge absolutely if for some real or complex number . Similarly, an improper integral of a function, is said to converge absolutely if the integral of the absolute value of the integrand is finite—that is, if

Absolute convergence is important for the study of infinite series because its definition is strong enough to have properties of finite sums that not all convergent series possess, yet is broad enough to occur commonly. (A convergent series that is not absolutely convergent is called conditionally convergent.)

Read more about Absolute Convergence:  Background, Relation To Convergence, Rearrangements and Unconditional Convergence, Products of Series, Absolute Convergence of Integrals

Famous quotes containing the word absolute:

    War is bestowed like electroshock on the depressive nation; thousands of volts jolting the system, an artificial galvanizing, one effect of which is loss of memory. War comes at the end of the twentieth century as absolute failure of imagination, scientific and political. That a war can be represented as helping a people to “feel good” about themselves, their country, is a measure of that failure.
    Adrienne Rich (b. 1929)