Find the sum 2 + 6 + 18 + 54 + ...

Step by step

The question

Question: find the sum 2 + 6 + 18 + 54 + and so on.

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

1 Find the ratio

2 Look at the sums

3 is not less than 1.

The terms do not get smaller.

So the sums grow without end.

Let's add the terms one at a time, and write each running sum: 2, 8, 26, 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.