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^{(n+1)}(c) (x-a)

^{n+1}/(n+1)! for c belongs to [a,x]

However, there are numerous cases in which I am only given a sigma summation form of an unknown function. If I want to find the nth degree error term (assume nth degree is the nth term in the summation), do I simply take the (n+1)th term? I personally do not agree with this since the n+1 th term is not necessarily the biggest. In normal situations I always re-evaluate the n+1 th derivative and find its max value, but with unknown functions I am not able to do that.

Any explanation on how to find the error bound? Do I need to find the n+1 th derivative every time?