Abel's Test - Abel's Test in Real Analysis

Abel's Test in Real Analysis

Suppose the following statements are true:

  1. is a convergent series,
  2. {bn} is a monotone sequence, and
  3. {bn} is bounded.

Then is also convergent.

Read more about this topic:  Abel's Test

Famous quotes containing the words test, real and/or analysis:

    “In my utter impotence to test the authenticity of the report of my senses, to know whether the impressions they make on me correspond with outlying objects, what difference does it make, whether Orion is up there in heaven, or some god paints the image in the firmament of the soul?”
    —Ralph Waldo Emerson (1803–1882)

    “The real price of everything, what everything really costs to the man who wants to acquire it, is the toil and trouble of acquiring it.”
    —Adam Smith (1723–1790)

    “Cubism had been an analysis of the object and an attempt to put it before us in its totality; both as analysis and as synthesis, it was a criticism of appearance. Surrealism transmuted the object, and suddenly a canvas became an apparition: a new figuration, a real transfiguration.”
    —Octavio Paz (b. 1914)