Sum from i = 2 to 6 of (i^2 - 1)

Step by step

The question

Question: work out the sum for i = 2 to 6 of (i² − 1).

1 Read the sigma

Σ is the Greek letter sigma.

It means: add up.

Start with i = 2, and stop at i = 6.

That is 6 − 2 + 1: 5 terms.

For each i we work out i² − 1.

Careful!

From 2 to 6 there are 5 terms, not 4: we count both ends.

So 6 − 2 + 1.

2 Write the terms

i = 2: we put 2 in place of i.

We get 3.

i = 3 gives 8.

And i = 6 gives 35.

That is the last one.

3 Add them

Now we add the 5 terms.

So the sum is 85.

4 Check

Let's check: we add them again, backwards.

We get 85 again.

It works!

Let's look back.

First: read the sigma.

Then: write the terms.

Then: add them.

Last: check.