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Math Help - find convergent set of the power series

  1. #1
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    find convergent set of the power series

    find the convergent set of the power series.

    heres the equation for problem2: http://img297.imageshack.us/img297/6606/untitledoy2.jpg
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  2. #2
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    Use the ratio test,
    \frac{n+2}{n+1}\to 1
    Thus, the radius of convergence is the reciprocal of that, namely, 1.
    Thus,
    |x|<1
    Is absolute convergence.
    Check endpoints x=\pm 1.
    For x=1 have an incomplete harmonic series thus it diverges.
    And for x=-1 we have an incomplete alterning harmonic thus it converges.
    [-1,1)
    Is the interval of convergence.
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  3. #3
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    thankyou.
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