In a proof by mathematical induction, we “start with a first step” and then prove that we can always go from one step to the next step. We can use this same idea to define a sequence as well. We can t...In a proof by mathematical induction, we “start with a first step” and then prove that we can always go from one step to the next step. We can use this same idea to define a sequence as well. We can think of a sequence as an infinite list of numbers that are indexed by the natural numbers. Another way to define a sequence is to give a specific definition of the first term and then state how to determine the next term in terms of previous terms; this process is known as definition by recursion.
In a proof by mathematical induction, we “start with a first step” and then prove that we can always go from one step to the next step. We can use this same idea to define a sequence as well. We can t...In a proof by mathematical induction, we “start with a first step” and then prove that we can always go from one step to the next step. We can use this same idea to define a sequence as well. We can think of a sequence as an infinite list of numbers that are indexed by the natural numbers. Another way to define a sequence is to give a specific definition of the first term and then state how to determine the next term in terms of previous terms; this process is known as definition by recursion.
