Yeah, I was aware of a direct relation to differentiation:

And I've extended the definition of the series to:

And I've found a beautiful return:

Converges for values as high as 30. My computer overflows before it stops converging.

I think my assumptions were correct. If this is true, I might find an infinite convergent power series for ln(x)

edit:

sadly, doesn't converge for values less than 1

And I've extended the definition of the series to:

And I've found a beautiful return:

Converges for values as high as 30. My computer overflows before it stops converging.

I think my assumptions were correct. If this is true, I might find an infinite convergent power series for ln(x)

edit:

sadly, doesn't converge for values less than 1