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Thread: Question about series

  1. #1
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    Question about series

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

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

    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 $\displaystyle \sum x_{n+1}-x_{n}$

    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; Mar 9th 2011 at 06:32 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 $\displaystyle f_n$ is increasing in $\displaystyle \left(\frac 1{n+1},\frac 1n\right)$.
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  3. #3
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    Since fn increasing on the interval , so $\displaystyle x_{n+1}-x_{n} > 0 $

    right ??
    but how we can find $\displaystyle 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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