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:
“A test of what is real is that it is hard and rough. Joys are found in it, not pleasure. What is pleasant belongs to dreams.”
—Simone Weil (19091943)
“A peoples literature is the great textbook for real knowledge of them. The writings of the day show the quality of the people as no historical reconstruction can.”
—Edith Hamilton (18671963)
“... 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 (18671945)