#51 in practice book

[yachoo]

hi, I was a bit confused about answer choice : the open region between two parallel lines. who can help me account for it?

[kdilks]

For reference, the question is "Let D be the region of the xy plane in which sum (x+2k)^k /k converges. The interior of D is...
a) open disc
b) bounded by ellipse
c) bounded by quadrilateral
d) between two parallel lines
e) half plane

Well, you know that the sum of z^k/k only converges when |z|<1 (or z=-1). Thus, this sum converges when |x+2y|<1. That corresponds to the open region between the lines x+2y=-1 and x+2y=1. The line x+2y=-1 is the other part of the region of convergence, but it's on the boundary, not the interior.

[mraudiofreak]

My friend and I decided the answer was wrong. We think it should the region should be between two parallel lines but neither open nor closed

[kdilks]

It specifically asks for the INTERIOR of the region, which would just be the open part.