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How to Use Sigma Notation

For adding up long series of numbers like the rectangle areas in a left, right, or midpoint sum, sigma notation comes in handy. Here’s how it works. Say you wanted to add up the first 100 multiples of 5 — that’s from 5 to 500. You could write out the sum like this:

5 + 10 + 15 + 20 + 25 + … + 490 + 495 + 500

But with sigma notation (sigma is the 18th letter of the Greek alphabet), the sum is much more condensed and efficient, and you’ve got to admit it looks pretty cool:


This notation just tells you to plug 1 in for the i in 5i, then plug 2 into the i in 5i, then 3, then 4, and so on all the way up to 100. Then, you add up the results. So that’s 5 · 1 plus 5 · 2 plus 5 · 3, and so on, up to 5 · 100. This is the same thing as writing out the sum the long way. By the way, the letter i has no significance. You can write the sum with a j,


or any other letter you like.

Here’s another example. If you want to add up


you can write the sum with sigma notation as follows:


There’s really nothing to it.