@mathematics.proofs 24 September 2020 more from that month

How to get the sum to infinity of a geometric series

In my last mathematical post I revealed **how to get the general rule for the sum of a geometric series**. In this article, I'll be demonstrating how to work with the general rule to come up with **the sum to infinity of a geometric series**. https://tinyurl.com/y2juhg2z When there is a sum to infinity of a geometric series - we can say it is **convergent**. 'Convergent' basically means the series will **tend to a specific value** as **more terms are added to it**. **Now, the sum to infinity of a geometric series will exist if these terms are met:** -1 < r < 1 **Like written in the previous article:** a = First term r = Common ratio **When you have the general rule:** S_n = [a(1-r^n)]/(1-r) If -1 < r < 1, r^n -->0, as n-->∞ **Therefore:** S_∞ = [a(1-0)]/(1-r) = a/(1-r) When |r| < 1 In the two videos below, ****the mathematics above is explained clearly****. These videos are worth watching if you haven't understood the mathematics yet. Video 1: How to Find the General Term for the Sum of the first 'n' terms of a Geometric Series https://youtu.be/__KeHwZR75E **Video 2: How to get the sum to infinity of a geometric series** https://youtu.be/gm4LtbPW7HY If this article has been useful to you, do not forget to subscribe to my read.cash page for more at: https://read.cash/@mathematics.proofs You can follow me on social media at: https://www.instagram.com/tiago_hands My Youtube channel can be found at: https://www.youtube.com/c/mathsvideosforweb/videos *Lead image: By* *Mehmet Turgut Kirkgoz* *from Pixabay* https://pixabay.com/users/tkirkgoz-16692474/?utm_source=link-attribution&utm_medium=referral&utm_campaign=image&utm_content=5551641