In this chapter we explored sequences and mathematical induction. At first these might not seem entirely related, but there is a link: recursive reasoning. When we have many cases (maybe infinitely many), it is often easier to describe a particular case by saying how it relates to other cases, instead of describing it absolutely. For sequences, we can describe the \(n\)th term in the sequence by saying how it is related to the previous term. When showing a statement involving the variable \(n\) is true for all values of \(n\text{,}\) we can describe why the case for \(n = k\) is true on the basis of why the case for \(n = k-1\) is true.
in-context