# Sequences & series intro

Contents

Sequences are like chains of ordered terms. Series are sums of terms in sequences. These simple innovations uncover a world of fascinating functions and behavior.

12 exercises available

In this tutorial, we'll review what sequences are, their associated notation, and formulas of sequences.

Now that we understand what a sequence is, we're going to think about what happens to the terms of a sequence at infinity (do they approach 0, a finite value, or +- infinity?).

You're familiar with sequences and have been eager to sum them up. Well wait no longer! In this tutorial, we'll see that series are just sums of sequences and familiarize ourselves with the notation.

A finite geometric series is the sum of the first few terms of a geometric sequence. It turns out there's a quick way of finding such a sum, without having to really sum all the terms one-by-one.

Partial sums are another way to think of finite series. Why partial? Because they are a part of an infinite series! Thinking of the partial sums of an infinite series helps us analyze the infinite series itself.

This might seem unbelievable at first, but for a certain class of geometric sequences, we can take the sum of all the infinite terms in the sequence and end up with a finite number! This sum is called an infinite geometric series. Learn when and how it can be found.

Learn how to find the value of some special classes of series. This material is relatively advanced and isn't included in the AP Calculus course.