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)
“All appointments hurt. Five friends are made cold or hostile for every appointment; no new friends are made. All patronage is perilous to men of real ability or merit. It aids only those who lack other claims to public support.”
—Rutherford Birchard Hayes (1822–1893)
“... 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)