Problems Plus 5: Infinite Sum of Vector Projections is a Geometric Series

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In this video I find the sum of an infinite series of consecutive magnitudes of vector projections and show it turns out to be just a geometric series. I first calculate the magnitudes for the first few vector projections and realize it follows a distinct pattern. This allows us to write the sum as a geometric series, thus we can just use the formula for the sum of a convergent geometric series. At the end of the video I also go over a quick recap and visual illustration of the geometric series.

Timestamps:

• Problem 4: Sum of vector projections: 0:00
• Solution: Recap on the dot and vector projections: 0:48
• Calculate projections to find a pattern: 2:26
• General equation for the magnitude of the n-th vector: 12:50
• Infinite sum of the magnitude of the n-th vector: 15:09
• Sum is a geometric series: 17:46
• Sum is equal to 20: 18:59
• Recap on the Geometric series: 19:43

Video notes and playlists:

• HIVE notes: https://peakd.com/hive-128780/@mes/jlgigkdl
• Full video and playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0G_7Jd6ZORHFQMk8jbwmkos
• Vectors and the Geometry of Space playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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