Previous page : Proof that ratios of Fibonacci successive numbers tend to the Golden ratio

Next page : Lagrange´s error term

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 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.

Previous page : Proof that ratios of Fibonacci successive numbers tend to the Golden ratio

Next page : Lagrange´s error termLast modified: