Oh dear. I just figured it out.
We shouldn't be finding the Maclaurin series for sin(1/x^2) at all. It should be for sin(x) first (with x0=0), then we let x=1/x^2 afterwards. Silly me...
I decided to put my attempt at a solution before the question, because the "solution" is what my question is about.
Homework Statement
Find the rate of convergence for the following as n->infinity:
lim [sin(1/n^2)]
n->inf
Let f(n) = sin(1/n^2) for simplicity.
2. The attempt at a...