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 final test of a novel will be our affection for it, as it is the test of our friends, and of anything else which we cannot define.”
    —E.M. (Edward Morgan)

    “No; we have been as usual asking the wrong question. It does not matter a hoot what the mockingbird on the chimney is singing.... The real and proper question is: Why is it beautiful?”
    —Annie Dillard (b. 1945)

    “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)