Abel's Test in Real Analysis
Suppose the following statements are true:
- is a convergent series,
- {bn} is a monotone sequence, and
- {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 is always how we treat the poor.”
—Robert Frost (1874–1963)
“Patience, to hear frivolous, impertinent, and unreasonable applications: with address enough to refuse, without offending; or, by your manner of granting, to double the obligation: dexterity enough to conceal a truth, without telling a lie: sagacity enough to read other people’s countenances: and serenity enough not to let them discover anything by yours; a seeming frankness, with a real reserve. These are the rudiments of a politician; the world must be your grammar.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“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)