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Convergent Series

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A convergent series is a series for which partial sums become arbitrarily close to some fixed number.

Convergent series is a college-level concept that would be first encountered in a Calculus II course. It is an Advanced Placement Calculus BC topic and is listed in the California State Standards for Calculus.

Examples

Geometric Series: A geometric series is a series in which the ratio of any two consecutive terms is always the same.
Taylor Series: A Taylor series is a power series of a function around a given point.

Prerequisites

Convergent: (1) An analysis, convergent means tending towards some definite finite value. (2) In the theory of continued fractions, a convergent is a partial sum of continued fraction terms.
Series: In mathematics, a series is an (often infinite) sum of terms specified by some rule.

Classroom Articles on Calculus II (Up to College Level)

  • Arc Length
  • Power Series
  • Exponential Growth
  • Radius of Convergence
  • Harmonic Series
  • Ratio Test
  • Maclaurin Series
  • Surface of Revolution