Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

trying to find the power series expansion of $\frac{z^2}{1-z}$ around the point $z_0=0$ and having some trouble doing so. So far I've tried the following idea:

Let $\frac{z^2}{1-z} = z^2(\frac{1}{1-z})$. Then the expansion of $z^2$ is $\sum_{n=2}^2 z^n$ (???) and the expansion of $\frac{1}{1-z}$ is $\sum_{n=0}^\infty z^n$. But I'm not sure if this is valid, or how to evaluate the product.

Am I on the right track, or should I be going about this differently?

share|cite|improve this question
I'm really don't understand... Before learning complex analysis, one most take single-variable-calculus course, or I'm wrong here? – Salech Alhasov Oct 15 '12 at 3:07
up vote 5 down vote accepted

You’re over-complicating things. You have the main piece, that $$\frac1{1-z}=\sum_{n\ge 0}z^n\;;$$ now just multiply by $z^2$ to get $$\frac{z^2}{1-z}=z^2\sum_{n\ge 0}z^n=\sum_{n\ge 0}z^{n+2}=\sum_{n\ge 2}z^n\;.$$

share|cite|improve this answer
Sheesh, wish I wouldn't have wasted so much time on this - either way, at least I don't have to waste any more! Thanks! – user44184 Oct 15 '12 at 3:02
@user44184: You’re welcome! – Brian M. Scott Oct 15 '12 at 3:03

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.