Yesterday finished with:

Can we expand this further?

Well, applying the product rule

And we know and

So,

Applying L’Hospital’s rule again:

And

This process can continue – delivering higher order derivatives on each iteration. It even starts to look like we might generate the factoral terms, as now we can see:

###### Related articles

- Taylor series expansions and L’Hospital’s rule (cartesianproduct.wordpress.com)
- Euler’s Identity, Part Two [EvolutionBlog] (scienceblogs.com)

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