Date: Feb 20, 2013 7:04 PM
Author: Dave Rudolf
Subject: Convergence arctan taylor searies
I was looking at the taylor series that is commonly used to compute
arc-tangent, which is
atan(x) = x - x^3/3 + x^5/5 - x^7/7 + x^9/9....
However, the domain for arc-tangent is +/- infinity. So, for x values
that are a bit larger than 1 (or smaller than -1), I don't see how
this series converges to anything. For instance, if I did atan(2),
then (2)^n will grow a lot faster than n itself, so each term will be
larger than the last.
Or am I missing something here?