Double Summation Result: \alpha^i\alpha^j

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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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Express it as an iterated sum and then apply the result for a sum of a geometric series. What do you get?
 
micromass said:
Express it as an iterated sum and then apply the result for a sum of a geometric series. What do you get?
Well actually i have the final result but simply i couldn't get the same answer using geometric sum. Here is the final result:
##\frac{2\alpha}{(1+\alpha)(1-\alpha)^2}##

How is it possible.
 
Have you tried anything? Where are you stuck?
 

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