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:
“We do not quite say that the new is more valuable because it fits in; but its fitting in is a test of its value—a test, it is true, which can only be slowly and cautiously applied, for we are none of us infallible judges of conformity.”
—T.S. (Thomas Stearns)
“The real question isn’t whether you love your kids or not, but how well you are able to demonstrate your love and caring so that your children really feel loved.”
—Stephanie Martson (20th century)
“... 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)