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:
“Unless the people can choose their leaders and rulers, and can revoke their choice at intervals long enough to test their measures by results, the government will be a tyranny exercised in the interests of whatever classes or castes or mobs or cliques have this choice.”
—George Bernard Shaw (18561950)
“A cynic might conclude that the real purpose of the $500 million-a-year implant business is the implantation of fat in the bellies and rumps of underemployed plastic surgeons.”
—Barbara Ehrenreich (b. 1941)
“Cubism had been an analysis of the object and an attempt to put it before us in its totality; both as analysis and as synthesis, it was a criticism of appearance. Surrealism transmuted the object, and suddenly a canvas became an apparition: a new figuration, a real transfiguration.”
—Octavio Paz (b. 1914)