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April 17th, 2010, 01:02 PM  #1 
Newbie Joined: Apr 2010 Posts: 1 Thanks: 0  Double integrad into geometric series problem
Hey all, I have a double integrand 1/(1xy) [0,1], [0,1] . My task is to show it is equivalent to series 1/n^2 where n=1 , goes to infinity. I know you have to turn it into a geometric series, which involves 1/1u and u=xy but I don't know much else. Thanks in advance. 
April 18th, 2010, 06:22 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,965 Thanks: 1606 
For 1 ? u < 1, 1/(1  u) = 1 + u + u² + u³ + . . ., a geometric series. Hence for 1 ? xy < 1, 1/(1  xy) = 1+ xy + x²y² + x³y³ + . . ., and you should be able to evaluate the double integral of each term in that series quite easily. 

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double, geometric, integrad, problem, series 
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