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Math Help - Interval/Radius of Convergence and Taylor Series help please?

  1. #1
    Junior Member
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    Interval/Radius of Convergence and Taylor Series help please?



    This series is convergent from x=? to x=?
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    This series is convergent from x=? to x=?
    __________________________________________________ __________________




    The radius of convergence is R=?

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    The Taylor series for at is
    Find the first few coefficients.
    c0=?
    c1=?
    c2=?
    c3=?

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    Please Help,
    Thank You

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  2. #2
    MHF Contributor Calculus26's Avatar
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    For ck(x-a)^k

    R = limck/c(k+1) or solve limc(k+1)/ck < 1


    Where k+1 is the subscript of ck

    This guarantees convergence |x-a| < R

    or a-R < x < a+R

    check x =a-R, a+R in the original for convergence to determine Interval of conv
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