Complex Analysis Clarification Question

[RJLiberator]

Homework Statement

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.

Homework Equations

Not available for this type of question. All information given.

The Attempt at a Solution

PDF

 

[fzero]

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?

That is correct.

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.

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.

 

[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.