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 (1909–1943)
“Discourage litigation. Persuade your neighbors to compromise whenever you can. Point out to them how the nominal winner is often a real loser—in fees, expenses, and waste of time. As a peacemaker the lawyer has a superior opportunity of being a good man. There will still be business enough.”
—Abraham Lincoln (1809–1865)
“Ask anyone committed to Marxist analysis how many angels on the head of a pin, and you will be asked in return to never mind the angels, tell me who controls the production of pins.”
—Joan Didion (b. 1934)