Sum from k = 2 to 5 of k^2

Step by step

The question

Question: work out the sum for k = 2 to 5 of k².

1 Read the sigma

Σ is the Greek letter sigma.

It means: add up.

Start with k = 2, and stop at k = 5.

That is 5 − 2 + 1: 4 terms.

For each k we work out k².

Careful!

From 2 to 5 there are 4 terms, not 3: we count both ends.

So 5 − 2 + 1.

2 Write the terms

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

We get 4.

k = 3 gives 9.

And k = 5 gives 25.

That is the last one.

3 Add them

Now we add the 4 terms.

So the sum is 54.

4 Check

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

We get 54 again.

It works!

Let's look back.

First: read the sigma.

Then: write the terms.

Then: add them.

Last: check.