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Math Help - Power series from -1 to -infinity?

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    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 <br />
|z-z_0| < \frac{1}{L} \implies \frac{1}{|z-z_0|} > L. But...that can't be sufficient...
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by davismj View Post
    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 <br />
|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.
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    Quote Originally Posted by Drexel28 View Post
    Really? Why don't you try running with it for a while.


    Thanks for the tip. Does that look sufficient?
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by davismj View Post


    Thanks for the tip. Does that look sufficient?
    Right idea, but be careful of what you called w. Take one more look!
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    Quote Originally Posted by Drexel28 View Post
    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.
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