(Solution) - Project Euler formulas in Terms of Jumps withut Integration -(2025 Original AI-Free Solution)

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Project Euler formulas in Terms of Jumps withut Integration; show that for a function whose third derivative is identically zero, where n = 1, 2, ??? and we sum over all the jumps js, j's, j''s of f, f', f', respectively, located at xs.