Sum from i = 1 to 5 of 2i Step by Step

Step by step

The question

Question: work out the sum for i = 1 to 5 of 2i.

Σ_{i = 1}⁵2i

1 Read the sigma

Σ is the Greek letter sigma.

It means: add up.

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

That is 5 − 1 + 1: 5 terms.

For each i we work out 2i.

Σ = add up

start: i = 1, stop: i = 5

5 − 1 + 1 = 5 terms

2 Write the terms

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

We get 2.

i = 1: 2(1) = 2

i = 2 gives 4.

i = 2: 2(2) = 4

i = 3: 2(3) = 6

i = 4: 2(4) = 8

And i = 5 gives 10.

That is the last one.

i = 5: 2(5) = 10

3 Add them

Now we add the 5 terms.

Σ_{i = 1}⁵2i = 2 + 4 + 6 + 8 + 10

So the sum is 30.

= 30

4 Check

Let's check with the pairs from the sequences lesson.

The terms go up by the same amount, so first plus last, 2 + 10, times 5 terms, over 2.

Pairs: 5 × (2 + 10)2 = 5 × 122 = 30

We get 30 again.

It works!

Let's look back.

First: read the sigma.

Then: write the terms.

Then: add them.

Last: check.

Answer