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 test of a given phrase would be: Is it worthy to be immortal? To make a beeline for something. Thats worthy of being immortal and is immortal in English idiom. I guess Ill split is not going to be immortal and is excludable, therefore excluded.”
—Robert Fitzgerald (19101985)
“He will watch from dawn to gloom
The lake-reflected sun illume
The yellow bees in the ivy-bloom,
Nor heed nor see, what things they be;
But from these create he can
Forms more real than living man,
Nurslings of immortality!”
—Percy Bysshe Shelley (17921822)
“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 (18381918)