Problems Plus 14: NEXT LEVEL Algebraic Manipulation for a Division of 2 P-Series

1 year ago
248
math education stem p-series absolutely convergent sequences and series mathematics science convergent series alternating series algebra

In this video I solve the division of two p-series and perform some truly amazing algebraic manipulations to simplify and solve the problem. I start off by realizing that the division involves absolutely convergent 2 p-series since p is greater than 1. If a series is absolutely convergent than it is also convergent, that is the alternating positive and negative signs won't affect the convergence. I perform some truly amazing algebraic manipulations on the top series to get it in the form of the bottom one, and which results in obtaining our starting expression. After some cancellations, we can then obtain a final simplified answer. Truly amazing stuff!

The timestamps of key parts of the video are listed below:

- Problem 14: 0:00
- Solution: 0:46
- NEXT LEVEL algebraic manipulation: 2:42
- Final answer: 11:31

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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