Problems Plus 9: Taking Multiple Derivatives of the Geometric Series

3 months ago

In this video I go over the sum of an infinite series that involves taking multiple derivatives of the Geometric Series. Starting off with the Geometric Series for x^n, we can apply the derivative to it for its radius of convergence, as derived from my earlier video on Power Series. When taking derivatives, the Radius of Convergence remains the same but we still have to determine the endpoints separately. The series with the terms (n^3)x^n has a radius of convergence equal to 1 and diverges at the endpoints, that is it diverges at x = 1 and x = -1.

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

Problem 9: 0:00
Solution: Start with a Geometric Series: 0:20
Differentiating with Quotient Rule: 6:42
Radius of Convergence is 1: 16:40
Checking for convergence at the endpoints: 18:18
Endpoints diverge: 21:09

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

Congratulations!

You have obtained a vote from CHESS BROTHERS PROJECT

✅ Good job. Your post has been appreciated and has received support from CHESS BROTHERS ♔ 💪

♟ We invite you to use our hashtag #chessbrothers and learn more about us.

♟♟ You can also reach us on our Discord server and promote your posts there.

♟♟♟ Consider joining our curation trail so we work as a team and you get rewards automatically.

♞♟ Check out our @chessbrotherspro account to learn about the curation process carried out daily by our team.

🥇 If you want to earn profits with your HP delegation and support our project, we invite you to join the Master Investor plan. Here you can learn how to do it.

Kindly

The CHESS BROTHERS team

0.000