 Σ notation is a quick way of showing how to add a sequence of numbers. The Greek letter Σ is used in math to represent adding. More precisely, it means 'find the sum of'. Σ (1,2,3,4,5) means 1 + 2 + 3 + 4 + 5 = 15 The notation is very specific about which numbers to add. For example:  means:"For all numbers xi, where i varies from 1 to 4, find the sum" or stated another way: "Find the sum of x1 + x2 + x3 + x4" whatever they are. Here's an actual example:  This means "fill in one through four for k, which is squared, and add the four terms": = 12 + 22 + 32 + 42 = 1 + 4 + 9 + 16 = 30
Here's another one:  This means "fill in numbers three through five for i, which are powers of 2, and add them": = 23 + 24 +25 = 8 + 16 + 32 = 56
And one more:  means "fill in 0 through 3 for i and add the terms":   Here's one in reverse: "Find the sum of all terms 0.5k3, where k is replaced by the values 2 through 6. Write it in summation notation first". Here it is:  = 0.5(2)3 + 0.5(3)3 + 0.5(4)3 + 0.5(5)3 + 0.5(6)3 = 220All of this can be entered into a calculator, so there is no need for partial answers. One final note: As you learn more about summation notation and how it is used, the following fact will be useful:
So for example:  will have 9 - 2 + 1 = 8 numbers to add will have 7 - 4 + 1 = 4 terms to add will have 5 - 0 + 1 = 6 terms to add
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will have b - a + 1 numbers to add