Math Easy Solutions | True-False Quiz Question 16: Monotonic Sequence Theorem @mes | Uploaded February 2024 | Updated October 2024, 4 hours ago.
In this video I show that a sequence is convergent, by the Monotonic Sequence Theorem, if it is positive and decreasing for all values of n. This would mean that the sequence is bounded because the largest value would be the initial term and the smallest value is a number greater than 0. Thus we can apply the Monotonic Sequence Theorem and the sequence is convergent. We can see this visually since the terms of the sequence will approach a limit L greater than 0. Thus, the answer to our question is True.
Time stamps:
- Question 16: 0:00
- Solution: True: 0:23
- Monotonic Sequence Theorem: 0:43
Full video below:
- Infinite Sequences and Series: Review and True-False Quiz: youtu.be/F0dsQLdXXpI
- HIVE video notes: peakd.com/hive-128780/@mes/infinite-sequences-and-series-review-and-true-false-quiz
- Video sections playlist: youtube.com/playlist?list=PLai3U8-WIK0FCqXVJv1r7eJvrvphfkr6L
Related Videos:
Infinite Sequences and Series playlist: youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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In this video I show that a sequence is convergent, by the Monotonic Sequence Theorem, if it is positive and decreasing for all values of n. This would mean that the sequence is bounded because the largest value would be the initial term and the smallest value is a number greater than 0. Thus we can apply the Monotonic Sequence Theorem and the sequence is convergent. We can see this visually since the terms of the sequence will approach a limit L greater than 0. Thus, the answer to our question is True.
Time stamps:
- Question 16: 0:00
- Solution: True: 0:23
- Monotonic Sequence Theorem: 0:43
Full video below:
- Infinite Sequences and Series: Review and True-False Quiz: youtu.be/F0dsQLdXXpI
- HIVE video notes: peakd.com/hive-128780/@mes/infinite-sequences-and-series-review-and-true-false-quiz
- Video sections playlist: youtube.com/playlist?list=PLai3U8-WIK0FCqXVJv1r7eJvrvphfkr6L
Related Videos:
Infinite Sequences and Series playlist: youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
------------------------------------------------------
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