Sum from i = 1 to 4 of 2^i

Step by step

The question

Question: work out the sum for i = 1 to 4 of 2 to the power i.

1 Read the sigma

Σ is the Greek letter sigma.

It means: add up.

Start with i = 1, and stop at i = 4.

That is 4 − 1 + 1: 4 terms.

For each i we work out 2 to the power i.

2 Write the terms

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

We get 2.

i = 2 gives 4.

And i = 4 gives 16.

That is the last one.

3 Add them

Now we add the 4 terms.

So the sum is 30.

4 Check

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

We get 30 again.

It works!

Let's look back.

First: read the sigma.

Then: write the terms.

Then: add them.

Last: check.