How to get the Sum to Infinity of a Geometric Series with Open Office

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4 years ago

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In my previous posts I demonstrated *How to find the general term for the first 'n' terms of a geometric series* and also *How to get the sum to infinity of a geometric series*. You can see those articles by clicking on the links.

In this post I'll be sharing with you how to get the sum to infinity of a geometric series on Open Office. To do that, you'll require a formula, and I'll be showing you exactly how to get that formula.

The formula for the general term for the first 'n' terms of a geometric series is:

S_n = [a(1-r^n)]/(1-r)

Whereby 'a' is the first term and 'r' is the common ratio. Although it is useful on paper there is not much that can be done with it on Open Office. To be able to use it on Open Office, it needs to be turned into a formula specifically for Open Office.

We do that by changing the formula above into:

1st Step

=SUM([a(1-r^n)]/(1-r))

2nd Step

=SUM((a*(1-r^(n)))/(1-r))

3rd Step

'n' is the letter we use to specify the number of terms we're dealing with. If we are dealing with 5 terms, for instance, n has to be equal to 5. Since we're working with Open Office, the value of terms will be placed inside a cell. So, if you place 5 inside the cell A1, and use the formula below:

=SUM((a*(1-r^(A1)))/(1-r))

You will be able to get the sum of the first 5 terms of a geometric series whereby the first term is 'a' and the common ratio is 'r'. Say for example a=4, r=1/3 and n=20 and 20 was placed inside the cell A1, the formula to use to get the right calculation would be:

=SUM((4*(1-(1/3)^(A1)))/(1-(1/3)))

And this could be simplified like so:

=SUM((4*(1-(1/3)^(A1)))/(2/3))

Sum to infinity

If you want to get the sum for various numbers of terms, like 1,2,3,4,5,6 and so on - all you do is use the simple drag down features that come with Open Office. Also, if -1 < r < 1 whereby 'r' is the common ratio, you'll end up with a convergent series, otherwise known as a sum to infinity.