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Math Help - [SOLVED] Complex Analysis: Limits!!!

  1. #1
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    Post [SOLVED] Complex Analysis: Limits!!!

    What is the limit and n tends to infintity of
    z+z^2+z^3+...+z^n
    note z belongs to the complex plane and is defined on the disc with centre 0 and radius 1.

    I think it should be 1/(1-z) but I cant see why.

    Thanks
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  2. #2
    Junior Member
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    Quote Originally Posted by syster View Post
    What is the limit and n tends to infintity of
    z+z^2+z^3+...+z^n
    note z belongs to the complex plane and is defined on the disc with centre 0 and radius 1.

    I think it should be 1/(1-z) but I cant see why.

    Thanks

    use this fact: the sum is equal to {z(1-z^{n+1})}/(1-z) where n-> \infty. The expression can be expanded to z/(1-z)+z^{n+2}/(1-z) taking the limit n-> \infty second term vanishes. That's it!
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