Hello, I'm not trying to solve this exact problem although mine is similar and I am confused on how they were able to get a -1 in the exponent from one step to another.
I have attached a picture indicating the step that I am confused about. How are they able to manipulate the series and pull out that -1 into the exponent thereby finding the residue?
The Attempt at a Solution
Some sort of series manipulation that I can't figure out; any help is greatly appreciated, thank you guys!