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 face we see was never young,
Nor could it ever have been old.
For he, to whom we had applied
Our shopmans test of age and worth,
Was elemental when he died,
As he was ancient at his birth:”
—Edwin Arlington Robinson (18691935)
“Fine art is the subtlest, the most seductive, the most effective instrument of moral propaganda in the world, excepting only the example of personal conduct; and I waive even this exception in favor of the art of the stage, because it works by exhibiting examples of personal conduct made intelligible and moving to crowds of unobservant unreflecting people to whom real life means nothing.”
—George Bernard Shaw (18561950)
“Ask anyone committed to Marxist analysis how many angels on the head of a pin, and you will be asked in return to never mind the angels, tell me who controls the production of pins.”
—Joan Didion (b. 1934)