My Math Forum Double integrad into geometric series problem

 Calculus Calculus Math Forum

 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/(1-xy) [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 1/1-u 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.

 Tags double, geometric, integrad, problem, series

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post poochie03 Algebra 3 March 18th, 2012 09:25 AM The Chaz Real Analysis 11 February 7th, 2011 04:52 AM cindyyo Algebra 2 August 24th, 2008 01:25 AM clooneyisagenius Real Analysis 1 January 30th, 2008 12:50 AM xela95 Calculus 5 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top