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)

    Here come real stars to fill the upper skies,
    And here on earth come emulating flies....
    Robert Frost (1874–1963)

    Ask anyone committed to Marxist analysis how many angels on the head of a pin, and you will be asked in return to never mind the angels, tell me who controls the production of pins.
    Joan Didion (b. 1934)