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:
“The first reading of a Will, where a person dies worth anything considerable, generally affords a true test of the relations’ love to the deceased.”
—Samuel Richardson (1689–1761)
“We are beginning a new era in our government. I cannot too strongly urge the necessity of a rigid economy and an inflexible determination not to enlarge the income beyond the real necessities of the government.”
—Andrew Jackson (1767–1845)
“The spider-mind acquires a faculty of memory, and, with it, a singular skill of analysis and synthesis, taking apart and putting together in different relations the meshes of its trap. Man had in the beginning no power of analysis or synthesis approaching that of the spider, or even of the honey-bee; but he had acute sensibility to the higher forces.”
—Henry Brooks Adams (1838–1918)