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 way of paradoxes is the way of truth. To test Reality we must see it on the tight-rope. When the Verities become acrobats we can judge them.”
—Oscar Wilde (1854–1900)
“...one of my motivating forces has been to recreate the world I know into a world I wish I could be in. Hence my optimism and happy endings. But I’ve never dreamed I could actually reshape the real world.”
—Kristin Hunter (b. 1931)
“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)