Review Question 3: Geometric Series and p-Series

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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/np 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:

Related Videos:

Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .


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