The order of error of a numerical method

[asmani]

Homework Statement

Find the order of error of this numerical method:

$$f''(x_i+\frac{h}{2})\simeq \frac{\Delta ^2f_i}{h^2}$$

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.

 

[asmani]

Solved!