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Can someone please explain how summing quantities of x^2 equals (1/3)x^3? …

Can someone please explain how summing quantities of x^2 equals (1/3)x^3? …

Can someone please explain how summing quantities of x^2 equals (1/3)x^3?
This summation process can be eliminated by using (1/3)x^3. Can you please show me the process in detail that one would use to prove this? Could you give me a geometrical example?

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