Series Tests

The Nth term of a series, the different test of convergence of series such as comparison test of first type and second type, limit form of the comparison test, the convergence(or divergence) of p-series, integral test, ratio test, Cauchy's root test, Cauchy's condensation test, Raabe's test, Logarithmic test, Kummer's test, Gauss's test, De Morgan and Bertrand's test along with their general forms are described briefly. Abel's theorem is also described. Each test is illustrated through examples.

21 topics

74 lectures

Educators

Course Curriculum

Integration Review

5 videos

Differential Equations

2 videos

Area Between Curves

2 videos

4 videos

Arc Length and Surface Area

3 videos

Integration Techniques

3 videos

6 videos

Trig Substitution

3 videos

Integrating Rational Functions

3 videos

Improper Integrals

3 videos

7 videos

5 videos

5 videos

Comparison Tests

2 videos

Root and Ratio Tests

4 videos

Alternating Series Test

2 videos

Converge Or Diverge Review

1 videos

2 videos

4 videos

Parametric Equations

4 videos

Polar Coordinates

4 videos

Series Tests Lectures

Series Tests

Series Tests - Intro

In mathematics, a series is a sum of the terms of an infinite sequence of numbers, often called the terms of the series. The sum of a series of numbers may not always be exactly equal to the overall series.

Jessica Wellington

Series Tests

Nth Term

A series is a sum of the terms of a sequence. The terms of a series are called its terms. The term "series" is used in contrast with the related notion of a "function", which is a mapping from a set of inputs to a set of permissible outputs with an associated rule for computing the output for a given input.

Jessica Wellington

Series Tests

Integral Test

In mathematics, the integral test is a test used to determine whether a given function is differentiable at a given point. The test is used to decide whether a given function is differentiable at a point, or, if it is differentiable, to find the derivative of the function at the point of interest. The integral test is a generalization of the second derivative test.

Jessica Wellington

Series Tests

P Series

The P-series is used in thermodynamics to represent the pressure of a system. It is a series of thermodynamic potentials, each of which is defined in terms of state variables of a system.

Jessica Wellington

Series Tests

Review

A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

Jessica Wellington