Finding the Taylor series of a function

[Elbobo]

Homework Statement

[sorry about the formatting, I had no idea how I would latex the sigma notation]
Let f(x) = [n=1 to infinity] summation of (-1)ⁿ n² / 3ⁿ * (x+1)ⁿ

Find the Taylor series of f(x) centered at c = -1

Homework Equations

Taylor series defined by
[n=0 to infinity] summation of f⁽ⁿ⁾(c) / n! * (x-c)ⁿ

The Attempt at a Solution

I tried converting the original function into
the form $$f(x) = \frac{a_{n}}{1-r}$$
and using the table method to find a Taylor series but I ended up with the same series (no surprise...).

Can anyone help? I don't know how I'm supposed to convert the series into a Taylor series...

 

[hunt_mat]

I think that is a Taylor Series. Have you tried differentiating and setting x=-1 to find the coeffients?

Mat

 

[Elbobo]

I have, and I end up with the original series.
But if that were already a Taylor series, why would my professor waste a question to ask me to rewrite the series in the same exact way...