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 of an adventure is that when you’re in the middle of it, you say to yourself, “Oh, now I’ve got myself into an awful mess; I wish I were sitting quietly at home.” And the sign that something’s wrong with you is when you sit quietly at home wishing you were out having lots of adventure.”
—Thornton Wilder (1897–1975)
“Don’t let us make imaginary evils, when you know we have so many real ones to encounter.”
—Oliver Goldsmith (1728–1774)
“... 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)