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:
“It is commonly said ... that ridicule is the best test of truth; for that it will not stick where it is not just. I deny it. A truth learned in a certain light, and attacked in certain words, by men of wit and humour, may, and often doth, become ridiculous, at least so far, that the truth is only remembered and repeated for the sake of the ridicule.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“A bad short story or novel or poem leaves one comparatively calm because it does not exist, unless it gets a fake prestige through being mistaken for good work. It is essentially negative, it is something that has not come through. But over bad criticism one has a sense of real calamity.”
—Rebecca West (1892–1983)
“A commodity appears at first sight an extremely obvious, trivial thing. But its analysis brings out that it is a very strange thing, abounding in metaphysical subtleties and theological niceties.”
—Karl Marx (1818–1883)