Sequences and series are interesting in their own right but, for us, they're a lead in to a method of proof called "mathematical induction". The material in these lectures introduces ideas and methods that we'll need to write those kinds of proofs.
Video Lectures
Sequences are a special class of function whose domain is limited to integers. They're going to be a building block to a new method of proof called a "proof by induction". (lecture slides)
If we take the numbers in a sequence and add them together we get a new object called a series which has its own special "sigma notation". (lecture slides)
The sigma notation has some properties that will give us an opportunity to see examples of proofs that rely on keeping track of indexes. (lecture slides)
Sometimes we need to make changes to the starting (and ending) point of a series. We can do that by changing the index variable. (lecture slides)
