Laurent series and partial fractions

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Homework Statement



find the laurent series of sin(2z)/(z^3) in [z]>0

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The Attempt at a Solution


I am completely confused. I can understand some of the examples given on laurent series, like using partial fractions and then finding geometric series. Do I rewrite the denominator as 1-(z^3+1)? This one I'm totally confused on. Please help
 
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You don't need partial fractions here. Think of a way to write the sine function as a series.
 
Always remember that a Laurent series is unique, so if you can find a way to express a function as a power series, then it is the Laurent series.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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