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How to get the Sum to Infinity of a Geometric Series with Open Office
*Image by* *Jade_Palace* *from Pixabay* https://pixabay.com/users/Jade_Palace-5302175/?utm_source=link-attribution&utm_medium=referral&utm_campaign=image&utm_content=2293154 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. https://tinyurl.com/y2juhg2z https://tinyurl.com/y2dvfn4g 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. https://www.openoffice.org/ 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**. https://www.openoffice.org/ 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**. https://www.openoffice.org/ https://tinyurl.com/y2dvfn4g *Article written by:* *https://www.instagram.com/tiago_hands* *For more mathematics articles, subscribe to:* *https://read.cash/@mathematics.proofs*
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