https://play.3speak.tv/embed?v=mes/n4paxdaa In this video, I show that the infinite series xⁿ = x⁰ + x¹ + x² + ... is just a geometric series, and converges if the absolute value of x is less than 1. By common convention, x⁰ = 1, so the first term a is 1, and the common ratio is x, thus the sum is given by the formula 1/(1 - x). [3Speak](https://3speak.tv/watch?v=mes/geometric-series-sum-of-xn-634) - [YouTube](https://youtu.be/_O8-FooyFwA) - [Telegram](https://t.me/meslinks/35024) - [Notes](https://peakd.com/mathematics/@mes/infinite-series-definition-examples-geometric-series-harmonics-series-telescoping-sum-more) - [Playlist](https://www.youtube.com/playlist?list=PLai3U8-WIK0FfxN_I9trdgSnWtJS-6wK1) - [Sequences and Series](https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz) - [MES Links](https://mes.fm/links) #math #calculus #series #geometricseries #education ![5 x^n series.png](https://files.peakd.com/file/peakd-hive/mes/23tmmf7kiuQmyNJvLA9wb9U52upsBXSWpBvhd5zwHcnu3wEQh3UNAWEmGkD8ZGE9YhAuy.png) ### Timestamps - Example 5: Find the sum of the series xⁿ where |x| is less than 1 – 0:00 - Solution: x⁰ is defined as equal to 1 – 0:22 - Expanding the series yields a geometric series – 1:07 - Since the common ratio x has an absolute value less than 1, the series is convergent and equals the first term a / (1 - x) – 2:02 ------------------------------------------------------ Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate SUBSCRIBE via EMAIL: https://mes.fm/subscribe MES Links: https://mes.fm/links MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps --- ▶ [Watch on 3speak.tv](https://3speak.tv/watch?v=mes/geometric-series-sum-of-xn-634)

Uqualla Transformational Series 1