In Reply to: Week 4/5 notes posted by Alex on May 08, 2003 at 19:29:38:
>in Thm 12 (a) shall it state the formal power series is "absolutely divergent" for that value of x instead of simply "divergent."
If a series is divergent, then it is automatically absolutely divergent; divergence works in the reverse manner to convergence. (If you are divergent, then you are not convergent, so in particular you are not absolutely convergent, and are thus absolutely divergent).
Because of this, it's usually better to avoid using the phrase "absolutely divergent" as it is somewhat misleading, it sounds
stronger than divergence when in fact it is weaker. I prefer instead the phrase "not absolutely convergent".
Terry