Recursion Sequences and Mathematical Induction
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In this lesson, we will learn
- recursive sequences
- mathematical induction
- how to use mathematical induction
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.
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).
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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