## GR9768 Q 51

Forum for the GRE subject test in mathematics.
mathQ
Posts: 41
Joined: Thu Mar 25, 2010 12:14 am

### GR9768 Q 51

let D be the region in the xy plane in which the series

Summation (x+2y)^k / k converges.

then the interior of D is

A) an open disk
B) the open region bounded by an ellipse
C) the open region bounded by a quadrilateral
D) the open region bounded by 2 parallel lines
E) an open half plane

speedychaos4
Posts: 47
Joined: Mon Mar 22, 2010 2:42 am

### Re: GR9768 Q 51

is it D?

mathQ
Posts: 41
Joined: Thu Mar 25, 2010 12:14 am

### Re: GR9768 Q 51

speedychaos4 wrote:is it D?

Yes, can you explain ? Thanks

speedychaos4
Posts: 47
Joined: Mon Mar 22, 2010 2:42 am

### Re: GR9768 Q 51

Use the ratio test, you can get r=|x+2y|, in order to ensure convergence, you want r<1, and therefore you have the ans.

mathQ
Posts: 41
Joined: Thu Mar 25, 2010 12:14 am

### Re: GR9768 Q 51

speedychaos4 wrote:Use the ratio test, you can get r=|x+2y|, in order to ensure convergence, you want r<1, and therefore you have the ans.
Great.

Thanks Speedy