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Recursion Sequences and Mathematical Induction




 
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More Lessons for Algebra

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A series of free, online Intermediate Algebra Lessons or Algebra II lessons.
Videos, worksheets, and activities to help Algebra students.

In this lesson, we will learn

  • recursive sequences
  • mathematical induction
  • how to use mathematical induction

Recursion Sequences

While arithmetic and geometric sequences involve a rule that uses a constant number, recursion sequences use the terms themselves in the rule. One term in recursion sequences is determined from using the terms before it. This concept of recursion sequences can be difficult to fully comprehend, but is found often in mathematics. For example, the Fibonacci sequence is a famous recursion sequence.

How to use a recursion formula to represent the Fibonacci sequence.

Recursive Sequences
In this sequence, we find the first few terms of two different recursive sequences ( that is, sequences where one term is used to find the next term, and so on).



Mathematical Induction

An important and fundamental tool used when doing proofs is mathematical induction. We can use mathematical induction to prove properties in math, or formulas. For example, we can prove that a formula works to compute the value of a series. Mathematical induction involves using a base case and an inductive step to prove that a property works for a general term.

This video explains how to prove a mathematical statement using proof by induction. There are two examples.

Proving an expression for the sum of all positive integers up to and including n by mathematical induction


 
Proof by Induction - Example 1
Proof by Induction - Example 2
Proof by Induction - Example 3


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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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