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Math Help - Radius and range of convergence

  1. #1
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    Radius and range of convergence

    Hi, can someone please tell me what is the radius and range of convergence of sum(100^k*(x-1)^(2*k)/k, k = 1 .. infinity) ?

    Any help would be greatly appreciated :-)
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  2. #2
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    Quote Originally Posted by Guardna View Post
    Hi, can someone please tell me what is the radius and range of convergence of sum(100^k*(x-1)^(2*k)/k, k = 1 .. infinity) ?

    Any help would be greatly appreciated :-)
    use the ratio test ...

    \lim_{k \to \infty} \left|\frac{a_{k+1}}{a_k} \right| < 1
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  3. #3
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    Quote Originally Posted by skeeter View Post
    use the ratio test ...

    \lim_{k \to \infty} \left|\frac{a_{k+1}}{a_k} \right| < 1

    Thank you sir!

    I was afraid of using the test of d'alembert because i thought k needed to start from 0 and not from 1.
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  4. #4
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    root test is faster, try it.
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  5. #5
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    It is indeed faster, thank you
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