Uploaded June 2026 | Updated September 2026, 3 weeks ago
In this video, I go over Theorem 2, which states that we can move a constant out of the sum of a series as well as add or subtract series individually. These follow from the Limit Laws of Sequences, and I use this to prove that the series involving an addition of terms is equal to an addition of the individual series. I go over an example, as well as make a note that a finite number of terms does not affect the convergence or divergence of a series.
#math #calculus #series #sequences #education
Timestamps:
- Theorem 2: Adding and subtracting convergent series – 0:00
- Proof of part ii of Theorem 2 via Limit Laws for Sequences – 1:54
- Taking the limit as the sum of partial sums approaches infinity – 3:55
- The series of sums is equal to the sum of the series – 6:23
- Example 9: Series of sums – 7:39
- Solution: The second series is a convergent geometric series that sums to 1 – 8:03
- The first series was solved from Example 6 via the telescoping sum and is equal to 3 – 9:42
- Adding the series obtains 3 + 1 = 4 as the sum – 11:00
- Note 4: A finite number of terms doesn't affect the convergence or divergence of a series – 11:40
Notes and playlists:
- Hive: 3speak.tv/watch?v=mes/theorem-2-series-of-sums-is-21
- 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 go over Theorem 2, which states that we can move a constant out of the sum of a series as well as add or subtract series individually. These follow from the Limit Laws of Sequences, and I use this to prove that the series involving an addition of terms is equal to an addition of the individual series. I go over an example, as well as make a note that a finite number of terms does not affect the convergence or divergence of a series.
#math #calculus #series #sequences #education
Timestamps:
- Theorem 2: Adding and subtracting convergent series – 0:00
- Proof of part ii of Theorem 2 via Limit Laws for Sequences – 1:54
- Taking the limit as the sum of partial sums approaches infinity – 3:55
- The series of sums is equal to the sum of the series – 6:23
- Example 9: Series of sums – 7:39
- Solution: The second series is a convergent geometric series that sums to 1 – 8:03
- The first series was solved from Example 6 via the telescoping sum and is equal to 3 – 9:42
- Adding the series obtains 3 + 1 = 4 as the sum – 11:00
- Note 4: A finite number of terms doesn't affect the convergence or divergence of a series – 11:40
Notes and playlists:
- Hive: 3speak.tv/watch?v=mes/theorem-2-series-of-sums-is-21
- 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
