d) Determine the Taylor series of f'(x) around x=0. Can you do so without using b)?
isn't it the same thing as b), just without the first term i guess?? or no?
You have,
$\displaystyle f(x)=\ln (1-x)$
And that,
$\displaystyle f'(x)=-\frac{1}{1-x}$
But this is a geometric series that you should recognize,
$\displaystyle -1+x-x^2+x^3-... = \sum_{k=0}^{\infty} (-1)^{k+1}x^k$
Last edited by ThePerfectHacker; Nov 26th 2006 at 06:58 PM.