Complex Analysis Clarification Question

1. Jul 18, 2015

RJLiberator

1. The problem statement, all variables and given/known data
Problem and solution found here: http://homepages.math.uic.edu/~dcabrera/math417/summer2008/section57_59.pdf

The question I am interested in is #1. In the solution, the instructor differentiates the series to get to:
2/(1-z)^3 = the series.

If I want the Maclaurin series of the function 1/(1-z)^3 then I would have to divide both sides here by 2.
Is this correct or am I missing something hidden? I ask because I believe the question asked for the series 1/(1-z)^3 and not the series of 2/(1-z)^3. So this may have been a mistake on the solutions.

2. Relevant equations
Not available for this type of question. All information given.

3. The attempt at a solution
PDF

2. Jul 18, 2015

fzero

That is correct.

Unless you can tell us exactly what the question asked for, we have no way to know. It may simply be that the instructor left the last step out since he knew you would realize that it just involved the division by 2.

3. Jul 18, 2015

RJLiberator

Excellent, thank you for the clarification. I assumed that to be the case, but I've seen some pretty tricky things with series so far and wanted to be sure.