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:

    “Unless the people can choose their leaders and rulers, and can revoke their choice at intervals long enough to test their measures by results, the government will be a tyranny exercised in the interests of whatever classes or castes or mobs or cliques have this choice.”
    —George Bernard Shaw (1856–1950)

    “O.J. Berman: Well, answer the question now. Is she or isn’t she?
    Paul: Is she or isn’t she what?
    O.J. Berman: A phony.
    Paul. I don’t know. I don’t think so.
    O.J. Berman: You don’t think so, huh? Well, you’re wrong. She is. But on the other hand, you’re right. Because she’s a real phony.”
    —George Axelrod (b. 1922)

    “A commodity appears at first sight an extremely obvious, trivial thing. But its analysis brings out that it is a very strange thing, abounding in metaphysical subtleties and theological niceties.”
    —Karl Marx (1818–1883)