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Question about understanding something in laurent series

  1. Dec 8, 2013 #1
    So the question I got the represention for both partial fractions after I broke the functions into two partial fraction one I got as 1/3(z + 1) + 2/3(z - 2) and I got laurent series represention for both but I was wondering for |z| < 1 how can they both converge for |z| < 1 are we acctually minusing both series from each other when we did that ? but when I got second series representation for second partial fraction I got - so that's how I understood since we are minusing |z| < 2 from |z| < 1 we get back to |z| < 1 I don't know if my intuition here is correct or wrong. but what if for second partial fraction we get a positive instead of a negative maybe here the negative that we got was by luck or something.
     

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