True-False Quiz Question 1: Series May or May NOT Converge if Limit of Terms = 0
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In this video I go over the first question of the True-False Quiz from my Calculus Book on infinite sequence and series, and show a series may or may not converge if the limit of the terms go to zero. Thus Question 1 is false. An example is the Harmonic series is a divergent p-series whose limit of the terms approach zero but the sum diverges to infinite. Note that the reverse is actually true, that is, if a series is convergent then the limit of the terms must approach zero.
Timestamps:
- Question 1: 0:00
- Solution: False: 0:42
- Note: Harmonic series is a divergent p-series: 1:47
This video was taken from my earlier video listed below:
- Infinite Sequences and Series: Review and True-False Quiz:
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-review-and-true-false-quiz
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FCqXVJv1r7eJvrvphfkr6L
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Infinite Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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