Obtain the following Taylor expansions. Give a general formula for the nth coefficient, and state the circle within which your expansion is valid.
expanded about z=0
Break the fraction down into parts using decomposition: f(x) = -1/(z+1) - 2/(z+2) then expand each seperatly. using -1/(1 + z) as your ratio you should notice the a1 term is -1 and the ratio is -z. thus the first one is SUM (a1)(-x)^n. Then repeat with the process with the second fraction.