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:

    “A test of what is real is that it is hard and rough. Joys are found in it, not pleasure. What is pleasant belongs to dreams.”
    —Simone Weil (1909–1943)

    “The real pleasure of being Mick Jagger was in having everything but being tempted by nothing ... a smouldering ill will which silk clothes, fine food, wine, women, and every conceivable physical pampering somehow aggravated ... a drained and languorous, exquisitely photogenic ennui.”
    —Anonymous “Chronicler.” Quoted in Philip Norman, The Life and Good Times of the Rolling Stones (1989)

    “Cubism had been an analysis of the object and an attempt to put it before us in its totality; both as analysis and as synthesis, it was a criticism of appearance. Surrealism transmuted the object, and suddenly a canvas became an apparition: a new figuration, a real transfiguration.”
    —Octavio Paz (b. 1914)