Calculus Basics
  • Introduction
  • ▶️Limit & Continuity
    • Limit properties & Limits of Combined Functions
    • Limits at infinity
    • All types of discontinuities
  • ▶️Differential Calculus
    • Differentiability
    • Local linearity & Linear approximation
    • Basic Differential Rules
    • Chain Rule
    • Derivatives of Trig functions
    • Implicit differentiation
    • Higher Order Derivatives
    • Derivative of Inverse functions
    • Derivative of exponential functions
    • Existence Theorems
    • L'Hopital's Rule
    • Critical points
      • Extrema: Maxima & Minima
      • Concavity
      • Inflection Point
    • Second Derivative Test
    • Anti-derivative
    • Analyze Function Behaviors with Derivatives
    • Optimization
    • Applications of Derivatives
      • Motion problems
      • Planar motion
  • ▶️Integral Calculus
    • Definite Integrals
    • Antiderivatives
    • Fundamental Theorem of Calculus (FTC)
    • Basic Integral Rules
    • Calculate Integrals
    • Integration using Trig identities
    • Improper Integral
    • U-substitution → Chain Rule
    • Integrate by Parts → Product Rule
    • Partial fractions → Log Rule
    • Trig-substitutions → Trig Rule
    • Average Value of Functions
  • ▶️Differential Equations
    • Parametric Equations Differentiation
    • Separable Differential Equations
    • Specific antiderivatives
    • Polar Curve Functions (Differential Calc))
    • Logistic Growth Model
    • Slope Field
    • Euler's Method
  • ▶️Applications of definite integrals
  • ▶️Series (Calculus)
    • Infinite Seires
    • Infinite Geometric Series
    • Convergence Tests
      • nth Term Test
      • Integral Test
      • p-series Test
      • Comparison Test
      • Ratio Test
      • Root Test
      • Alternating Series Test
    • Absolute vs. Conditional Convergence
      • Error Estimation of Alternating Series
      • Error Estimation Theorem
      • Interval of Convergence
    • Power Series
      • Taylor Series
      • Maclaurin Series
      • Lagrange Error Bound
      • Finding Taylor series for a function
      • Function as a Geometric Series
      • Maclaurin Series of Common functions
      • Euler's Formula & Euler's Identity
  • Multivariable functions
    • Parametric Functions
    • Partial derivatives
    • Gradient
Powered by GitBook
On this page
  • Divergent Test
  • Integral Test
  • p-series Test
  • Direct Comparison Test
  • Limit Comparison Test
  • Ratio Test
  • Root Test
  • Alternating Series Test
  • Absolute Convergence & Conditional Convergence
  1. Series (Calculus)

Convergence Tests

PreviousInfinite Geometric SeriesNextnth Term Test

Last updated 6 years ago

Here lists common Convergence Tests and overview of each. Details are singled out to each section.

Convergence test are a set of tests to determine wether the series CONVERGENT or DIVERGENT. It includes:

Test

Description

► Divergent Test

Take nth term's limit. (only to test divergence)

► Integral Test

Take limit of the series function's integration.

► p-series Test

Examine at the p value of 1/nᴾ.

► Comparison Test

Compare the series to a "similar" p-series or geometric-series.

► Ratio Test

Take limit of two terms ratio.

► Root Test

Take the limit of nth root of nth term.

► Alternating Test

Test if terms are decreasing, and take limit of nth term.

Divergent Test

Take the limit of nth term, if it's NOT ZERO, then it's DIVERGENT.

image

Integral Test

p-series Test

Direct Comparison Test

Compare the series to a "similar" p-series or geometric-series.

Limit Comparison Test

Compare the series to a "similar" p-series or geometric-series.

Ratio Test

Take limit of two terms ratio.

Root Test

Take the limit of nth root of nth term.

Alternating Series Test

Test if terms are decreasing, and take limit of nth term.

Absolute Convergence & Conditional Convergence

image
image
image
image
image
image
image
▶️