Uploaded June 2026 | Updated September 2026, 2 weeks ago
In this video, I show that the harmonic series, 1 + 1/2 + 1/3 + 1/4 + ..., diverges by showing its even power partial sums are greater than a similar but smaller series involving repeating 1/2 terms. This is a very clever derivation, and it was due to the French scholar Nicole Oresme from the 14th century.
#math #calculus #series #HarmonicSeries #education
Timestamps:
- Example 7: Show that the harmonic series is divergent – 0:00
- Solution: For this series, we will show that the even partial sums get larger – 0:26
- Writing each even partial sum as an inequality greater than a similar slightly smaller sum involving repeating terms of 1/2 – 2:01
- Pattern: The n-th partial sum is greater than 1 + n/2, which goes to infinity – 6:30
- The series of even power terms is divergent, therefore the harmonic series is divergent – 7:53
- This derivation is due to the French scholar Nicole Oresme (1323-1382) – 8:43
Notes and playlists:
- Hive: 3speak.tv/watch?v=mes/harmonic-series-proving-it-384
- 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 harmonic series, 1 + 1/2 + 1/3 + 1/4 + ..., diverges by showing its even power partial sums are greater than a similar but smaller series involving repeating 1/2 terms. This is a very clever derivation, and it was due to the French scholar Nicole Oresme from the 14th century.
#math #calculus #series #HarmonicSeries #education
Timestamps:
- Example 7: Show that the harmonic series is divergent – 0:00
- Solution: For this series, we will show that the even partial sums get larger – 0:26
- Writing each even partial sum as an inequality greater than a similar slightly smaller sum involving repeating terms of 1/2 – 2:01
- Pattern: The n-th partial sum is greater than 1 + n/2, which goes to infinity – 6:30
- The series of even power terms is divergent, therefore the harmonic series is divergent – 7:53
- This derivation is due to the French scholar Nicole Oresme (1323-1382) – 8:43
Notes and playlists:
- Hive: 3speak.tv/watch?v=mes/harmonic-series-proving-it-384
- 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
