Problems Plus 25: Differentiating Multiple Power Series

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1 year ago
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Health & Science Education math science power series term by term differentiation ratio test calculus stem mes mathematics

In this video I go over an interesting math problem which involves differentiating 3 power series to find relationships among them in order to show the given equation is true. In order to differentiate power series, we first need to determine if the series are convergent, which I do so using the Ratio Test. Next we can differentiate the given equation and using our obtained relationships, can show that the equation equals a constant. Plugging in x = 0 into the equation, we can thus simply solve for this constant, and thus prove our given equation.

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

- Problem 25: 0:00
- Solution: Using the Ratio Test to determine convergence: 1:33
- Term by Term Differentiation: 8:35
- Differentiating the desired equation: 14:42
- Determining the constant that equals to the desired equation: 20:09

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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