S₁, S₂, and S₃ represent the number of n terms, 2n terms, and 3n of the first term of the geometry series, prove that:
A. S₁ (S₃ - S₂) = (S₂ - S₁) ²
B. S₁² + S₂² = S₁ (S₂ + S₃)
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