Uploaded June 2026 | Updated September 2026, 3 weeks ago
In this video, I show that the infinite series x^n = x^0 + x^1 + x^2 + ... is just a geometric series, and converges if the absolute value of x is less than 1. By common convention, x^0 = 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).
#math #calculus #series #geometricseries #education
Timestamps:
- Example 5: Find the sum of the series x^n where |x| is less than 1 – 0:00
- Solution: x^0 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
Notes and playlists:
- 3Speak: 3speak.tv/watch?v=mes/geometric-series-sum-of-xn-634
- Hive Notes: peakd.com/mathematics/@mes/infinite-series-definition-examples-geometric-series-harmonics-series-telescoping-sum-more
- Playlist: youtube.com/playlist?list=PLai3U8-WIK0FfxN_I9trdgSnWtJS-6wK1
- Sequences and Series: youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz
- MES Links: https://mes.fm/links .
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In this video, I show that the infinite series x^n = x^0 + x^1 + x^2 + ... is just a geometric series, and converges if the absolute value of x is less than 1. By common convention, x^0 = 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).
#math #calculus #series #geometricseries #education
Timestamps:
- Example 5: Find the sum of the series x^n where |x| is less than 1 – 0:00
- Solution: x^0 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
Notes and playlists:
- 3Speak: 3speak.tv/watch?v=mes/geometric-series-sum-of-xn-634
- Hive Notes: peakd.com/mathematics/@mes/infinite-series-definition-examples-geometric-series-harmonics-series-telescoping-sum-more
- Playlist: youtube.com/playlist?list=PLai3U8-WIK0FfxN_I9trdgSnWtJS-6wK1
- Sequences and Series: youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz
- MES Links: https://mes.fm/links .
------------------------------------------------------
Become a MES Super Fan! 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: 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
