Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] f(x) = 2/x , a = −3
Your power series will be
$\displaystyle \displaystyle f(x) = \sum_{n = 0}^{\infty}\frac{f^{(n)}(a)}{n!}(x-a)$, where $\displaystyle \displaystyle f^{(n)}(x)$ represents the $\displaystyle \displaystyle n^{\textrm{th}}$ derivative of $\displaystyle \displaystyle f(x)$.
Why have you put $\displaystyle \displaystyle (x + 3)^n$ as the denominator? A polynomial does not have algebraic terms in denominators...
I suggest you reread what I posted above. You need to evaluate a number of derivatives at the point $\displaystyle \displaystyle x = -3$ and substitute these and $\displaystyle \displaystyle x = a = -3$ into the Taylor series formula.