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## Homework Statement

Find the order of error of this numerical method:

[tex]f''(x_i+\frac{h}{2})\simeq \frac{\Delta ^2f_i}{h^2}[/tex]

## Homework Equations

Taylor's theorem, Newton's interpolation polynomial and its error.

## The Attempt at a Solution

I started from Taylor's expansion at x_i and x_i+1 but didn't get anywhere.

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