determine the power seris in summnation notation

Question

f(x)= 1/x^2 and centered at a=2

Answer 1

Use the negative exponent notation to determine the derivatives.

You should easily see that the nth derivative is (-1)ⁿn!/xⁿ⁺²

This means the Taylor series is the sum from n=0 to ∞ of (-1)ⁿn!(x-2)ⁿ/2ⁿ⁺²