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GR9768 Q 51

Posted: Tue Apr 06, 2010 1:10 pm
by mathQ
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

Re: GR9768 Q 51

Posted: Tue Apr 06, 2010 1:28 pm
by speedychaos4
is it D?

Re: GR9768 Q 51

Posted: Tue Apr 06, 2010 1:31 pm
by mathQ
speedychaos4 wrote:is it D?

Yes, can you explain ? Thanks

Re: GR9768 Q 51

Posted: Tue Apr 06, 2010 1:49 pm
by speedychaos4
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.

Re: GR9768 Q 51

Posted: Tue Apr 06, 2010 2:02 pm
by mathQ
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