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:

    To answer a question so as to admit of no reply, is the test of a man.
    Ralph Waldo Emerson (1803–1882)

    Freedom is but the possibility of a various and indefinite activity; while government, or the exercise of dominion, is a single, yet real activity. The longing for freedom, therefore, is at first only too frequently suggested by the deep-felt consciousness of its absence.
    Karl Wilhelm Von Humboldt (1767–1835)

    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)