Applied Mathematics · Ch 5 — Sequences and Series
Sequences
Sequences
A sequence is simply an ordered list of numbers, each following a definite rule or pattern. Instead of a random collection, every term in a sequence has a specific position — first, second, third, and so on — which we denote by . This idea of order is what separates a sequence from a set: in a sequence, swapping two terms changes the sequence itself. Understanding how to spot the pattern and write the …
Series
A sequence is a list of numbers in a definite order, but a series is what you get when you actually add those numbers together. Instead of just writing , we write and ask: what is the sum? This shift from listing to summing is the heart of the chapter, and it opens the door to powerful shortcuts — …