Question

Find the sum of the following infinite geometric series, if it exists.
60 + 84 + 117.6 + 164.64 +…

Answer 1

The clue here is "if it exists". Do you know why it would not?

Answer 2

Because You cant Multiply or Divide

Answer 3

If you check, you will find dividing each term by the one before it gives a consistent ratio.

We could only find the sum if we were approaching some definite total. That happens when we keep adding less and less each time. What would make that happen?

Answer 4

Division... So It doesn't Exist

Answer 5

Division is what we do want. Check this series

1 + .5 + .25 + .125 + ...

I am dividing by 2 or multiplying by 1/2.

My totals look like this

1 1.5 1.75 1.875 ..... (Looks like I am headed to 2)

I keeping adding less and less. Eventually I will be adding about 0 (but not zero).

On the calculator it would look like I was adding zero.

So, when we have -1 < r < 1 we can get the sum using a very simple formula.

S(infinity) = (a1) / (1-r)