
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
April 17th, 2010, 02:02 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, 07:22 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,140 Thanks: 1415 
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. 

Tags 
double, geometric, integrad, problem, series 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Geometric Series  poochie03  Algebra  3  March 18th, 2012 10:25 AM 
Convergent series > series of geometric means converges  The Chaz  Real Analysis  11  February 7th, 2011 05:52 AM 
sequences and series: geometric series  cindyyo  Algebra  2  August 24th, 2008 02:25 AM 
Geometric series/target of series/etc...  clooneyisagenius  Real Analysis  1  January 30th, 2008 01:50 AM 
Geometric Series?  xela95  Calculus  5  December 31st, 1969 04:00 PM 