Abel's test, also called Abel's criterion, is a method for testing the convergence of an infinite series, named after the mathematician Niels Henrik Abel, who proved it in 1826. Two slightly different versions exist, one used with series of real numbers and the other with power series in complex analysis, and a related form, Abel's uniform convergence test, gives a criterion for the uniform convergence of a series of functions that depend on parameters.
Facts
StatementIf the series sum of a_n converges and b_n is a monotone bounded sequence, then the series sum of a_n b_n also converges. 1 Connections
Named After
Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Sources
1. Abel's test, Wikipedia
Real analysis test statement
Then ∑ a n b n is also convergent.
Historical statement
The test is named after mathematician Niels Henrik Abel, who proved it in 1826.
View the SourceReader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.