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 a given phrase would be: Is it worthy to be immortal? To “make a beeline” for something. That’s worthy of being immortal and is immortal in English idiom. “I guess I’ll split” is not going to be immortal and is excludable, therefore excluded.”
    —Robert Fitzgerald (1910–1985)

    “For if the proper study of mankind is man, it is evidently more sensible to occupy yourself with the coherent, substantial and significant creatures of fiction than with the irrational and shadowy figures of real life.”
    —W. Somerset Maugham (1874–1965)

    “Analysis as an instrument of enlightenment and civilization is good, in so far as it shatters absurd convictions, acts as a solvent upon natural prejudices, and undermines authority; good, in other words, in that it sets free, refines, humanizes, makes slaves ripe for freedom. But it is bad, very bad, in so far as it stands in the way of action, cannot shape the vital forces, maims life at its roots. Analysis can be a very unappetizing affair, as much so as death.”
    —Thomas Mann (1875–1955)