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November 11th, 2010, 03:16 AM  #1 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Series computation with residue theory! [color=#000000]Compute with the help of complex analysis the series .[/color] 
November 11th, 2010, 01:22 PM  #2 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Re: Series computation with residue theory! [color=#000000]A hint: Take the function and then the contour integral over the circle with radius with and center .[/color] 
November 13th, 2010, 08:38 AM  #3 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Re: Series computation with residue theory! [color=#000000]The function has a simple pole in every single with inside the circle mentioned above which we name . We will use the formula . For the left side of the boxed equation we have, . Letting we take the result, . The line integral goes to zero as n goes to infinity because is bounded , it can be proved easily.[/color] 

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