Find the sum 5 - 5 + 5 - 5 + ...

Step by step

The question

Question: find the sum 5 − 5 + 5 − 5 + and so on.

The dots at the end mean: it goes on forever.

1 Find the ratio

2 Look at the sums

1 is not less than 1.

The terms do not get smaller.

So the sums jump back and forth forever.

Let's add the terms one at a time, and write each running sum: 5, 0, 5, and so on.

So this series has no sum.

There is no answer: the running sums never settle.

Let's look back.

First: find the ratio.

Last: look at the sums.