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Double Summation

  1. Jun 28, 2015 #1
    what is the result for the following double summation:
    ##\sum\limits_{i \neq j}^{\infty}\alpha^i\alpha^j ##

    where ## i, j =0,1,2,.......##
     
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  3. Jun 28, 2015 #2

    micromass

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    Express it as an iterated sum and then apply the result for a sum of a geometric series. What do you get?
     
  4. Jun 28, 2015 #3
    Well actually i have the final result but simply i couldnt get the same answer using geometric sum. Here is the final result:
    ##\frac{2\alpha}{(1+\alpha)(1-\alpha)^2}##

    How is it possible.
     
  5. Jun 28, 2015 #4

    micromass

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    Have you tried anything? Where are you stuck?
     
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