So what is a Series? and how is it different than a Sequence?
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
Well, we already know that a Sequence is just a listing of numbers that follow a pattern.
A Series is simply the sum of the terms in a Sequence. That’s it!
Now, to represent the Sum we use Summation Notation or Sigma Notation, which is just a simple way of expressing the sum of the values of a sequence.
We will learn how to write Summation Notation for a Finite and Infinite Series, as well as to create Partial Sums for several Finite Series.
The process is easy!
Formula for the Sum of a Series
All we have to do is plug in numbers to whatever comes after the Sigma (Sum) Notation and add them up.
Or Sum it Up! as Math is Fun nicely states!
Then we will investigate some very important Summation Properties, that allow us simplify any given Series in order to find the sum quickly and succinctly. Using these newfound Summation Properties, we evaluate different Series and find the sum.
Lastly, we will learn how to Reindex a Series. This is a skill that is not always found in math textbooks, but it is a critical skill for future math courses like Calculus and Differential Equations.
So what is Reindexing?
Well, let’s say we want to add to Series together. But, one Series starts at n=1 and another Series that starts at n=0. But, because they don’t have the same starting point, we can’t add them together. Ugh!
Thankfully, we have an amazing Summation Property that allows us to adjust the indices and variables of sequences!
So, we will learn how to take a Series and reindex our lower and upper limits, as well as our variables to whatever number we desire! Trust me, it’s easy and it’s going to be super important in the future!
Writing Summation Notation – Video
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