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Thread: 206.11.02.67 a. Find the function represented by: b. Find the interval of convergence

  1. #1
    Super Member bigwave's Avatar
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    206.11.02.67 a. Find the function represented by: b. Find the interval of convergence

    $\tiny{206.11.02.67}\\$
    $\textit{Find the function represented by:} \\
    \textit{Find the interval of convergence}$
    \begin{align*}\displaystyle
    f_{67}(x)&=\sum_{k=0}^{\infty}
    \left[\frac{(x^2+1)}{4}\right]^k \\
    &=?
    \end{align*}
    wasn't sure about the function?
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  2. #2
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    Re: 206.11.02.67 a. Find the function represented by: b. Find the interval of converg

    Let r= \frac{x^2+ 1}{4}. Then the sum is \sum_{k=0}^\infty r^k which is a geometric series. Use the usual formula for the sum of the geometric series, \frac{1}{1- r}.
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    Re: 206.11.02.67 a. Find the function represented by: b. Find the interval of converg

    $\dfrac{x^2+1}{4} < 1 \Longrightarrow -\sqrt{3} < x < \sqrt{3}$
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  4. #4
    Super Member bigwave's Avatar
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    Cool Re: 206.11.02.67 a. Find the function represented by: b. Find the interval of converg

    much mahalo
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