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:

    “Tried by a New England eye, or the more practical wisdom of modern times, they are the oracles of a race already in its dotage; but held up to the sky, which is the only impartial and incorruptible ordeal, they are of a piece with its depth and serenity, and I am assured that they will have a place and significance as long as there is a sky to test them by.”
    —Henry David Thoreau (1817–1862)

    “I came back to myself,
    To the real work, to
    “What is to be done.””
    —Gary Snyder (b. 1930)

    “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)