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:
“To test a modest mans modesty do not investigate if he ignores applause, find out if he abides criticism.”
—Franz Grillparzer (17911872)
“Fear can supplant our real problems only to the extentunwilling either to assimilate or to exhaust itwe perpetuate it within ourselves like a temptation and enthrone it at the very heart of our solitude.”
—E.M. Cioran (b. 1911)
“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)