Sum from k = 1 to 5 of (k^2 + k)

Step by step

The question

Question: work out the sum for k = 1 to 5 of (k² + k).

1 Read the sigma

Σ is the Greek letter sigma.

It means: add up.

Start with k = 1, and stop at k = 5.

That is 5 − 1 + 1: 5 terms.

For each k we work out k² + k.

2 Write the terms

k = 1: we put 1 in place of k.

We get 2.

k = 2 gives 6.

And k = 5 gives 30.

That is the last one.

3 Add them

Now we add the 5 terms.

So the sum is 70.

4 Check

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

We get 70 again.

It works!

Let's look back.

First: read the sigma.

Then: write the terms.

Then: add them.

Last: check.