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Math Help - Question about series

  1. #1
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    Question about series

    Show that this function f_{n}(x)= x^{5}+nx-1
    has exactly real zero point and it is in the interval
    \left(\frac{1}{n+1},\frac{1}{n}\right)

    decide if the series \sum \left(-1\right)^{n-1} a_{n}
    converges absolutly or conditionally ??
    For which x converge the power series \sum a_{n}x^{n}?

    I tried to substitute the two end points of the interval for the x in the function by (intermediate value theorm)
    to show that we have exactly one zero point , is it useful to use this way ?
    After that i tried to take the \sum x_{n+1}-x_{n}

    Is it useful to solve the problem ?? I got a very complex function , i do not know if it is right to use intermediate value theorm .

    Does anyone have an idea ??
    Last edited by mariama; March 9th 2011 at 07:32 AM.
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  2. #2
    Super Member girdav's Avatar
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    Intermediate value theorem gives you that exists a zero, but not the fact there is exactly one. But f_n is increasing in \left(\frac 1{n+1},\frac 1n\right).
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  3. #3
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    Since fn increasing on the interval , so  x_{n+1}-x_{n} > 0

    right ??
    but how we can find  a_{n}
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  4. #4
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    I am a little confused
    but maybe because of the function is bounded and it has a limit . so it has a one zero point
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