Summing Arithmetic Sequences Visually (proof without words)
This is a short, animated visual proof demonstrating how to visualize the sum of an arithmetic sequence, producing a closed formula for such a sum.
This is visual is based on proofs known to the ancient Greeks and can be found in Roger B. Nelsen's book Icons of Mathematics (page 177):
https://bookstore.ams.org/dol-45
Specializing to a = 0 and d = 1 gives the sum of the first n integers (triangular numbers) formula. Specializing to a = 1 and d = 2 gives the sum of the odd integers (which yields the squares). In general, we can get any polygonal number formula from this fact (in addition to many others).
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Music in this video:
Prelude 2 by VGM Mark H | / user-656562764
Music promoted by https://www.free-stock-music.com
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