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:

    “The test of literature is, I suppose, whether we ourselves live more intensely for the reading of it.”
    —Elizabeth Drew (1887–1965)

    “That is Lenin. Look at the self-willed, stubborn head. A real Russian peasant’s head with a few faintly Asiatic lines. That man will try to overturn mountains. Perhaps he will be crushed by them. But he will never yield.”
    —Rosa Luxemburg (1871–1919)

    “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)