Name: True-False Quiz Question 1: Series May or May NOT Converge if Limit of Terms = 0
Uploaded: 2023-12-13T04:10:55+00:00
Duration: 3 min 3 s
Description: 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.

4 months ago

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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: https://youtu.be/F0dsQLdXXpI
- 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