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Infinite Series-Mathematics
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1 students

Infinite Series-Mathematics

Infinite Series-Mathematics P-Series test Comparison test D'Alberts ratio test Cauchy's nth root test
Last updated 2/2025
English

What you'll learn

  • Infinite Series
  • Comparison Test
  • D'Alberts Ration Test
  • Cauchy's nth root test
  • P-series test

Course content

3 sections28 lectures3h 2m total length
  • Introduction7:42
  • Lecture 22:48
  • Lecture 31:43
  • Lecture 47:20
  • Lecture 58:33
  • Lecture 69:48
  • Lecture 78:45
  • Lecture 87:20
  • Lecture 98:49
  • Lecture 1010:35
  • Lecture 116:04
  • Lecture 125:32

Requirements

  • Basic of Infinite series
  • Examples on Different test

Description

Infinite Series-Mathematics

P-Series test 

Comparison test 

D'Alberts ratio test

Cauchy's nth root test

An infinite series is the sum of infinitely many terms in a sequence.

The p-Series Test is a method used to determine the convergence or divergence of a p-series.

p-Series Convergence Criteria

  • If p>1, the series converges.

  • If p≤1, the series diverges.

    Comparison Test (Direct and Limit Forms)

    The Comparison Test is used to determine whether a series converges or diverges by comparing it to a known series.

    When to Use Each Test

    • Use Direct Comparison when one series clearly dominates the other.

    • Use Limit Comparison when the terms behave similarly but aren't directly comparable.

      Ratio Test

      The Ratio Test helps determine whether an infinite series

      ∑an converges or diverges by examining the ratio of consecutive terms.

      When to Use the Ratio Test

      The Ratio Test is especially useful for:

      • Factorial series (n!)

      • Exponential terms (a^n)

      • Power series

        Cauchy's nth Root Test (Radical Test)

        Cauchy’s nth Root Test is a convergence test for infinite series. It is useful when terms involve powers of n.

        When to Use the Root Test

        The Root Test is most effective for:

        • Exponential expressions

        • Terms with n raised to a power (like n^n)

        • Radicals or power series

Who this course is for:

  • Maths learning students
  • Students understand about convergence and divergence