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 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
Sum of integers
This visual proof by Ian Richards
Sum of squares
This visual proof by Martin Gardner