Math Tutorial 12.4 - Infinite Series Explained

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There are 7 lessons in this math tutorial covering Infinite Series Explained. The tutorial starts with an introduction to Infinite Series Explained and is then followed with a list of the separate lessons, the tutorial is designed to be read in order but you can skip to a specific lesson or return to recover a specific math lesson as required to build your math knowledge of Infinite Series Explained. you can access all the lessons from this tutorial below.

In this Math tutorial, you will learn:

  • What are finite and infinite series? How do you identify them?
  • What are diverging and converging series?
  • How do we find the sum of all terms in converging geometric series?
  • What is the comparison test of convergence?
  • What are some special types of infinite series?
  • What is the ratio convergence test? When do we use it?
  • What is the root convergence test? When do we use it?


So far, we have dealt with finite series (where the sum of all terms is easy to calculate) and with the sum of the first n terms of infinite series.

In this tutorial we will explain how to find the sum of all terms in some infinite series. This may seem impossible given that the series are infinite, i.e. their terms extend to infinity but we will explain that some infinite series converge to a certain value.

Please select a specific "Infinite Series Explained" lesson from the table below, review the video tutorial, print the revision notes or use the practice question to improve your knowledge of this math topic.

Sequences and Series Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
12.4Infinite Series Explained
Lesson IDMath Lesson TitleLessonVideo
12.4.1Infinite and Finite Number Series
12.4.2Converging and Diverging Infinite Series
12.4.3Calculating an Infinite Geometric Series
12.4.4The Comparison Test of Convergence
12.4.5The Special Types of Infinite Series
12.4.6The Ratio Convergence Test
12.4.7The Root Convergence Test

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  2. Sequences and Series Video tutorial: Infinite Series Explained. Watch or listen to the Infinite Series Explained video tutorial, a useful way to help you revise when travelling to and from school/college
  3. Sequences and Series Revision Notes: Infinite Series Explained. Print the notes so you can revise the key points covered in the math tutorial for Infinite Series Explained
  4. Sequences and Series Practice Questions: Infinite Series Explained. Test and improve your knowledge of Infinite Series Explained with example questins and answers
  5. Check your calculations for Sequences and Series questions with our excellent Sequences and Series calculators which contain full equations and calculations clearly displayed line by line. See the Sequences and Series Calculators by iCalculator™ below.
  6. Continuing learning sequences and series - read our next math tutorial: Working with Term-to-Term Rules in Sequences

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