Simple taylor expansion? (Complex)

Using

expand is a Taylor series about z=2.

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Do I just find all the derivatives or something? Perhaps I need to use a geometric series here? Partial fractions? How do I start?

EDIT: It also mentions I need the first four non-zero terms of the series.

Re: Simple taylor expansion? (Complex)

multiply top and bottom by 1/3 and re-express the function as 1/3*(-1/(2-z)/3) now substitute (2-z)/3 into the geometric expansion and the rest is algebra! God I wish I could express myself better symbolically. Much less messy than ProveIt's approach!