Statements (44)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
infinite series
|
| gptkbp:application |
gptkb:probability_theory
gptkb:signal_processing gptkb:Laurent_series gptkb:Taylor_series gptkb:Zeta_function Fourier series economics engineering quantum mechanics |
| gptkbp:convergesTo |
ratio test
comparison test integral test root test alternating series test |
| gptkbp:defines |
A sum of infinitely many terms, typically written as a_1 + a_2 + a_3 + ...
|
| gptkbp:example |
gptkb:harmonic_series
gptkb:geometric_series power series |
| gptkbp:field |
gptkb:mathematics
|
| https://www.w3.org/2000/01/rdf-schema#label |
Infinity Series
|
| gptkbp:importantFor |
gptkb:Abel's_theorem
gptkb:Weierstrass_M-test gptkb:Dirichlet's_test Cauchy convergence criterion |
| gptkbp:notation |
Σ (sigma notation)
|
| gptkbp:property |
can be absolutely or conditionally convergent
divergent series do not have a finite sum may converge or diverge partial sums form a sequence sum defined as limit of partial sums sum may be finite or infinite terms can be real or complex numbers can be rearranged (conditionally convergent series may change sum) |
| gptkbp:relatedConcept |
integer sequence
limit summation partial sum |
| gptkbp:usedIn |
analysis
calculus mathematical physics |
| gptkbp:bfsParent |
gptkb:Rodgers_Instruments
|
| gptkbp:bfsLayer |
7
|