In this video lesson we will gain an overview of sequences and series, and learn terms and definitions, such as convergence, divergence, factorial, monotonic, bounded, infinite, etc.
Definition of a Finite Sequence
First, we will investigate the differences between a sequence and a series.
A sequence is a function that has a set of natural numbers as its domain. All this means is that a sequence is a list of numbers. Whereas a series is the sum of a sequence. Simply put, a series adds all the terms in a sequence together.
Formula for the Sum of a Series
Next, we will learn how to generate general terms and simplify factorials for both finite and infinite sequence and series.
Additionally, we will discover the how to determine whether or not a sequence converges or diverges, using nth-term test for sequences, and use this knowledge to discuss how we are to determine the convergence of an infinite series.
Did you know that there are 9 different tests we can use in order to determine whether a series will converge or diverge?
Don’t worry, at the end of this lesson we will then learn the golden acronym for memorizing the series tests, and learn the order for how and when they are used.
Sequences and Series Intro Video
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