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:

    “There is held to be no surer test of civilisation than the increase per head of the consumption of alcohol and tobacco. Yet alcohol and tobacco are recognisable poisons, so that their consumption has only to be carried far enough to destroy civilisation altogether.”
    —Havelock Ellis (1859–1939)

    “Most of our occupations are low comedy.... We must play our part duly, but as the part of a borrowed character. Of the mask and appearance we must not make a real essence, nor of what is foreign what is our very own.”
    —Michel de Montaigne (1533–1592)

    “The spider-mind acquires a faculty of memory, and, with it, a singular skill of analysis and synthesis, taking apart and putting together in different relations the meshes of its trap. Man had in the beginning no power of analysis or synthesis approaching that of the spider, or even of the honey-bee; but he had acute sensibility to the higher forces.”
    —Henry Brooks Adams (1838–1918)