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:

    “Experimental work provides the strongest evidence for scientific realism. This is not because we test hypotheses about entities. It is because entities that in principle cannot be ‘observed’ are manipulated to produce a new phenomena
    [sic] and to investigate other aspects of nature.”
    —Ian Hacking (b. 1936)

    “There is only one real tragedy in a woman’s life. The fact that her past is always her lover, and her future invariably her husband.”
    —Oscar Wilde (1854–1900)

    “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)