Usually we prove results related to powers of sums algebraically. How can you illustrate geometrically powers of sums basically for powers 1,2,3 ?
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Sum of integers
This visual proof by Ian Richards
Sum of squares
This visual proof by Martin Gardner
Sum of cubes
This visual proof by Georg Schrage
you can find more elegant answers,👇
Proofs without words by Roger Nelsen and https://www.youtube.com/@MathVisualProofs