# Thread: Power series from -1 to -infinity?

1. ## Power series from -1 to -infinity?

I can't really think of any way to prove this. I think it starts with the fact that I'm not really sure what my desired outcome is. I was thinking there might be some way to get it in the form $\sum_{n=0}^{\infty } a_n(z-z_0)^n$. Also, it is very plain to see that $\frac{1}{L}$ is radius of convergence $\sum_{n=0}^{\infty } a_n(z-z_0)^n$, which, it seems, is somehow related since $
|z-z_0| < \frac{1}{L} \implies \frac{1}{|z-z_0|} > L$
. But...that can't be sufficient...

2. Originally Posted by davismj
Also, it is very plain to see that $\frac{1}{L}$ is radius of convergence $\sum_{n=0}^{\infty } a_n(z-z_0)^n$, which, it seems, is somehow related since $
|z-z_0| < \frac{1}{L} \implies \frac{1}{|z-z_0|} > L$
. But...that can't be sufficient...
Really? Why don't you try running with it for a while.

3. Originally Posted by Drexel28
Really? Why don't you try running with it for a while.

Thanks for the tip. Does that look sufficient?

4. Originally Posted by davismj

Thanks for the tip. Does that look sufficient?
Right idea, but be careful of what you called $w$. Take one more look!

5. Originally Posted by Drexel28
Right idea, but be careful of what you called $w$. Take one more look!
lol, yea that proof was crap. I rewrote it (but its still up above). Thanks for the tip. I was making it way harder than it had to be.