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:
“Experimental work provides the strongest evidence for scientific realism. This is not because we test hypotheses about entities. It is because entities that in principle cannot be ‘observed’ are manipulated to produce a new phenomena
[sic] and to investigate other aspects of nature.”
—Ian Hacking (b. 1936)
“The art of using moderate abilities to good advantage is a way of stealing the esteem of others, and often brings a man into greater reputation than does real merit.”
—François, Duc De La Rochefoucauld (1613–1680)
“Whatever else American thinkers do, they psychologize, often brilliantly. The trouble is that psychology only takes us so far. The new interest in families has its merits, but it will have done us all a disservice if it turns us away from public issues to private matters. A vision of things that has no room for the inner life is bankrupt, but a psychology without social analysis or politics is both powerless and very lonely.”
—Joseph Featherstone (20th century)