Name: True-False Quiz Question 2: Divergent p-series
Uploaded: 2023-12-19T05:05:19+00:00
Duration: 2 min 51 s
Description: In this video I go over the infinite series of the form n to the power of -sin 1 and show that is just a divergent p-series. The term n^(-sin 1) can be rewritten as 1/n^(sin 1) which is of the form 1/

1 year ago

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Health & Science Education math science p-series divergence convergence series sequences trig trigonometric series

In this video I go over the infinite series of the form n to the power of -sin 1 and show that is just a divergent p-series. The term n^(-sin 1) can be rewritten as 1/n^(sin 1) which is of the form 1/n^p where p is less than 1. We can plug sin 1 into the calculator, in both radians or degrees, and the value is going to be less than 1. Thus, we have a simple divergent p-series since p is less than 1. Hence the answer to the question is it is False, that is, it is NOT a convergent series.

Timestamps:

- Question 2: 0:00
- Solution: False: 0:18
- Calculation check: 1:24
- Divergent p-series with p is less than 1: 2:34

Full video 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