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:

    “A decent provision for the poor is the true test of civilization.”
    —Samuel Johnson (1709–1784)

    “I did not go to Boston, for with regard to that place I sympathize with one of my neighbors, an old man, who has not been there since the last war, when he was compelled to go. No, I have a real genius for staying at home.”
    —Henry David Thoreau (1817–1862)

    “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)