# Truncation Error and its Bounds

1. Jan 22, 2012

### theuniverse

1. The problem statement, all variables and given/known data
a) Derive a Taylor series with n+1 terms and the associated truncation error for
the function $$f(x)=(log(x)-x+1)/(x-1)^2$$
b) Construct an expression that bounds the truncation error, assuming n > 2, for a given value of x

2. The attempt at a solution
a) So I came up with the following series: (from k=2 to k=n+2) $$Ʃ((-1)^k*(x-1)^{k-1})/(k+1)$$

But I'm not really sure how to derive the truncation error. Is the error simply in the n+2 term, and all I have to do is just sub it into the Lagrange remainder equation?

b) not sure on what interval I should be doing it. As well as taking taking n+2 derivatives to figure out the bound doesn't seem right...