Interface InfiniteSeries<T>

All Known Implementing Classes:
GeometricSeries, HarmonicSeries, PowerSeries
public interface InfiniteSeries<T>
Represents an infinite series.

An infinite series is the sum of an infinite sequence of terms: S = Σ a(k), k=0..∞

Since:
1.0
Author:
Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

  • Method Summary

    Modifier and Type
    Method
    Description
    boolean
    isConvergent()
    Determines if this series is convergent.
    T
    limit()
    Returns the limit of the series if convergent.
    T
    partialSum(int n)
    Computes the partial sum of the first n terms.
    T
    term(int k)
    Returns the k-th term of this series.

  • Method Details

    • partialSum

      T partialSum(int n)
      Computes the partial sum of the first n terms.

      S_n = Σ a(k), k=0..n

      Parameters:
      n - the number of terms to sum (n ≥ 0)
      Returns:
      the partial sum S_n

    • isConvergent

      boolean isConvergent()
      Determines if this series is convergent.

      A series converges if lim(n→∞) S_n exists and is finite.

      Returns:
      true if convergent, false if divergent

    • limit

      T limit()
      Returns the limit of the series if convergent.

      L = lim(n→∞) S_n

      Returns:
      the limit L
      Throws:
      ArithmeticException - if the series is divergent

    • term

      T term(int k)
      Returns the k-th term of this series.
      Parameters:
      k - the term index (k ≥ 0)
      Returns:
      the term a(k)