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Let us start with the observation that

i.e. that

We continue with the fact that

or

Now we substitute that into the expression for *f*(*x*) to get

We repeat this process again with

This gives us

Repeating this over and over again using the more general

We get

I.e. the Taylor series expansion with *k*+1 terms plus some strange integral in the end. On the next page we will find an upper bound (biggest possible value) of the last term, called the error term.

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