How do i figure out this problem about taylor series?

Question

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 Rsubn(x) -> 0.]
f(x)= lnx, a=2

Answer 1

Just start differentiating. f' = 1/x, f'' = -1/x^2, and so on.

Then plug in 2 for each of those x's, use the definition of Taylor Series, and you're set.