infinite series
Unbounded additive sequence
An infinite series is a sum of infinitely many terms, written as a sequence that continues without end.
In mathematics, such series may converge to a finite value or diverge to infinity: The infinite series 1 + 1/2 + 1/4 + 1/8... converges to 2.
Calculus relies heavily on infinite series to represent functions and calculate limits.
computation
Adding to find total
- approximationNear but inexact value
- truncationCutting something shorter
- algorithmFinite problem-solving procedure
- recursionProcess invoking itself
convergence
Maximum allowed extent
- sumAddition's result
- boundedConfined within limits
- monotonicUnchanging in direction
- telescopingSliding sections that compact
theory
e^(ix) relates to trigonometry
- Bernoulli numbersRational sequence in analysis
- transcendentalBeyond ordinary experience
- number theoryPure math studying integers
- AbelHebrew name meaning breath
divergence
Having no limits
- oscillationRepeated back-and-forth movement
- regularizationPenalty preventing model complexity
summation
Adding to find total
- approximationNear but inexact value
- truncationCutting something shorter
- algorithmFinite problem-solving procedure
limit
Maximum allowed extent
generating function
Formal series encoding sequences
Euler's formula
e^(ix) relates to trigonometry
- Bernoulli numbersRational sequence in analysis
- transcendentalBeyond ordinary experience
- number theoryPure math studying integers
unbounded
Having no limits
- oscillationRepeated back-and-forth movement
- regularizationPenalty preventing model complexity
- Infinityendless, eternal, boundless, limitless, forever
- Formulaschemical formula, quadratic formula, empirical formula, area formula, volume formula
- pi calculation
- math historyEuclid, Pythagoras, Newton, Leibniz, Euler
- number typesprime numbers, natural numbers, whole numbers, integers, rational numbers
- ArchimedesArchimedes screw, eureka, eureka moment, buoyancy, hydrostatics
series, infinity, infinite, serial, indefinite, undefined, indefinitely, infinitesimal, serially