Abel's Test - Abel's Test in Real Analysis

Abel's Test in Real Analysis

Suppose the following statements are true:

  1. is a convergent series,
  2. {bn} is a monotone sequence, and
  3. {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:

    “We do not quite say that the new is more valuable because it fits in; but its fitting in is a test of its value—a test, it is true, which can only be slowly and cautiously applied, for we are none of us infallible judges of conformity.”
    —T.S. (Thomas Stearns)

    “The danger of crippling thought, the danger of obstructing the formation of the public mind by specially suppressing ... representations is far greater than any real danger that there is from such representations.”
    —George Bernard Shaw (1856–1950)

    “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)