Hi everyone and welcome to MathSux! In this post we are going to go over summation notation (aka sigma notation). The summing of a series isn’t hard as long as you know how to read the notation! We will go over an example and breakdown what each part of this notation represents step by step. When you are ready, please don’t forget to check out the practice questions at the end of this post to truly master the topic. Thanks for stopping by and happy calculating! 🙂
What is Summation Notation?
Summation notation lets us write a series in an easy and short-handed way. Before we go any further we also need to define a series!
Series: The sum of adding each term within an infinite sequence. This can include arithmetic or geometric sequences we are already familiar with. For example, let’s say we have the arithmetic sequence: 2,4,6,8, ….. now with a series we are adding all of these terms together: 2+4+6+8+……
Now back to summations. Summations allow us to quickly understand that the sequence being added together is done so on an infinite or finite basis by giving us a range of values for which the unknown variable can be evaluated and summed together. Summation notation is represented with the capital Greek letter sigma, Σ, with numbers below and above as limits for calculation and the series that must be evaluated to the right.
If this sounds confusing, don’t worry, it might sound more confusing than it actually is! Take a look at the breakdown for sigma notation below:
Wait, what does the above summation say?
Translation: It tells us to evaluate the expression, n+1 by plugging in 1 for n, 2 for n, and 3 for n and then wants us to sum all three solutions together.
Take a look below to see how to solve this step by step:
Check out the video above to see more examples step by step! When you’re ready to try them on your own, check out the practice problems below:
Practice Questions:
Solutions:
Still got questions? No problem! Don’t hesitate to comment with any questions below. Thanks for stopping by and happy calculating! 🙂
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Looking for something similar to sigma notation? Check out this post on geometric sequences here! If you’re looking for more statistics formulas, check out how to find expected value!
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