# Thread: Prove that F'(z) = f(z) by Power Series expansion.

1. ## Prove that F'(z) = f(z) by Power Series expansion.

Please focus on 19-b) at the bottom. I'm not sure how hard this is supposed to be, or where $\displaystyle |z-z_0| < R$ comes in. I think I must be missing something.

Thanks!

2. Originally Posted by davismj

Please focus on 19-b) at the bottom. I'm not sure how hard this is supposed to be, or where $\displaystyle |z-z_0| < R$ comes in. I think I must be missing something.

Thanks!
You need the fact that $\displaystyle |z-z_0|< R$ to ensure that your move of the derivative from outside the sum to inside was kosher.

3. Originally Posted by Drexel28
You need the fact that $\displaystyle |z-z_0|< R$ to ensure that your move of the derivative from outside the sum to inside was kosher.
Can you explain (or give an example or something) of why it wouldn't work if $\displaystyle |z-z_0| > R$?

Actually, nevermind. I'm being lazy, I know this one.

As always, Thanks!

Also, are you really an undergraduate freshman?