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:
“There is a parallel between the twos and the tens. Tens are trying to test their abilities again, sizing up and experimenting to discover how to fit in. They don’t mean everything they do and say. They are just testing. . . . Take a good deal of your daughter’s behavior with a grain of salt. Try to handle the really outrageous as matter-of-factly as you would a mistake in grammar or spelling.”
—Stella Chess (20th century)
“O.J. Berman: Well, answer the question now. Is she or isn’t she?
Paul: Is she or isn’t she what?
O.J. Berman: A phony.
Paul. I don’t know. I don’t think so.
O.J. Berman: You don’t think so, huh? Well, you’re wrong. She is. But on the other hand, you’re right. Because she’s a real phony.”
—George Axelrod (b. 1922)
“... the big courageous acts of life are those one never hears of and only suspects from having been through like experience. It takes real courage to do battle in the unspectacular task. We always listen for the applause of our co-workers. He is courageous who plods on, unlettered and unknown.... In the last analysis it is this courage, developing between man and his limitations, that brings success.”
—Alice Foote MacDougall (1867–1945)