Name: Review Question 3: Geometric Series and p-Series
Uploaded: 2023-11-10T04:33:26+00:00
Duration: 5 min 36 s
Description: In this video I go over a quick review of geometric series and p-series and show the circumstances for when they are convergent. A geometric series has all the terms being a constant number multiplied

2 years ago

190

Health & Science Education math calculus science stem geometric series sequences p-series similar triangles

In this video I go over a quick review of geometric series and p-series and show the circumstances for when they are convergent. A geometric series has all the terms being a constant number multiplied by a common ratio starting from the power of 0 and incrementing by 1 for each successive term. The series is convergent and equal to the (first term) / (1 - common ratio) when the absolute value of the common ratio is less than 1. I also show a geometric interpretation of the geometric series using similar triangles.

A p-series is of the form 1/n^p and it is convergent when p is greater than 1 and divergent for all other values.

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

- Question 3: 0:00
- Solution to (a): Geometric series: 0:28
- Geometric representation via similar triangles: 2:04
- Solution to (b): p-Series: 4:51

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