I'm trying to understand how the second divided difference is formulated. I understand that the first divided difference is just the equation of a slope.(adsbygoogle = window.adsbygoogle || []).push({});

[itex]f(x_{i},x_{i+1})=\frac{f(x_{i})-f(x_{i+1})}{x_{i}-x_{i+1}}[/itex]

Every source that I have read always jumps to the second divided difference by saying "and by induction"

[itex]f(x_{i},x_{i+1},x_{i+2})=\frac{f(x_{i},x_{i+1})-f(x_{i+1},x_{i+2})}{x_{i+2}-x_{i+1}}[/itex]

How is induction used to get this equation?

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# Derivation of 2nd divided difference

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