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:

    This, then, is the test we must set for ourselves; not to march alone but to march in such a way that others will wish to join us.
    Hubert H. Humphrey (1911–1978)

    It were a real increase of human happiness, could all young men from the age of nineteen be covered under barrels, or rendered otherwise invisible; and there left to follow their lawful studies and callings, till they emerged, sadder and wiser, at the age of twenty-five.
    Thomas Carlyle (1795–1881)

    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)