The order of error of a numerical method

asmani
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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.
 
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Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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