See how that works? We took every value of k between 2 and 5 inclusive, and substituted each into the expression then we added everything up.Īs a bonus, once you understand sigma notation, you understand Big Pi notation for free: a Big Pi ( ) works exactly the same as a Big Sigma, except it denotes multiplication instead of addition (‘P’ is for ‘product’). If you’re still confused, don’t worry an example should make things clear! For each value of k between a and b, f(k) will be some value which gives one term in the sum. f(k): this is the expression that describes each term in the sum.a, b: a is the starting index and b is the ending index.It will take on all the integer values between a and b (inclusive). k: The k on the left side of the equals is called the index variable or the index of summation, or sometimes just the index.It is not an ‘E’! Sigma corresponds to the English letter ‘S’ ‘S’ is for ‘sum’. : this is a capital sigma, the eighteenth letter of the Greek alphabet. Let’s go through each part of that and see what they mean in more detail: This results in a bunch of values which we add up. We would read this as “the sum, as k goes from a to b, of f(k).” In plain English, what this means is that we take every integer value between a and b (inclusive) and substitute each one for k into f(k). Here’s what a typical expression using sigma notation looks like: First, let’s talk about the sum of a constant. To do that, we will need to know some basic sums. Calculating with sigma notation We want to use sigma notation to simplify our calculations. k1k1k1 n Property 2(Distribution).XXcakcak. Write the following sum in sigma notation. nn Property 1(Commutativity).XX(ak+bk) Xak+bk. Although it can appear scary if you’ve never seen it before, it’s actually not very difficult. Because sigma notation is just a new way of writing addition, theusual properties of addition still apply, but a couple of the importantones look a little dierent. Sigma notation provides a way to compactly and precisely express any sum, that is, a sequence of things that are all to be added together.
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