How to Remember Sigma Notation

∑ … the most confusing letter

Many students will be familiar with the feeling of terror that the simple symbol ∑ can invoke. But it doesn’t need to be confusing, and in fact it is a very handy way to write sums.

Sigma. Generated by DALL·E 2

How I see sigma notation

I’m not going to get into a complicated description of what sigma notation means. Your textbook probably has that, or you can read it here.

I’m just going to explain how I see sigma notation:

When you see it like that, it is extremely simple. The lower limit, or the number you start with, is below the ∑. Usually a variable is defined there, such as k = 1. That is the variable you will plug the numbers in for when applying the formula. The upper limit, or the number you stop at, is above the ∑. And the formula to the right of the ∑ is what you need to apply when adding everything together.

So the steps are:

1. Plug the lower limit into the formula, substituting for the variable
2. Increase by 1 and plug the result into the formula, substituting for the variable again
3. Put a plus sign between each time you plug a number into the formula
4. Stop after you plug the upper limit into the formula
5. Add all of the results together

It might not make complete sense just yet, but hopefully the following examples help.

Start with a simple example

Let’s just start with a simple example to understand how sigma notation works. Here is a simple summation problem:

Here is what you need to do to get that answer:

You just have to start at the lower limit and go to the higher limit, adding 1 each time and substituting the answer in for n. Then just add up the each term to get the result.

Slightly more complex examples

Now that you know the basics of how to see sigma notation, here are some more complicated examples.

Try to cover the answer and write it out for yourself first.

Here is the answer with steps on how to get there:

Here’s another example:

After substituting the numbers and simplifying, you should get:

And that’s it!

Sigma notation is actually one of the easiest concepts in math to understand. It’s nothing to be afraid of.

Hopefully this helps and good luck with your future math studies!