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:

    There is held to be no surer test of civilisation than the increase per head of the consumption of alcohol and tobacco. Yet alcohol and tobacco are recognisable poisons, so that their consumption has only to be carried far enough to destroy civilisation altogether.
    Havelock Ellis (1859–1939)

    No genuine equality, no real freedom, no true manhood or womanhood can exist on any foundation save that of pecuniary independence. As a right over a man’s subsistence is a power over his moral being, so a right over a woman’s subsistence enslaves her will, degrades her pride and vitiates her whole moral nature.
    Susan B. Anthony (1820–1907)

    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)