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Math Help - is this convergent?

  1. #1
    Junior Member
    Joined
    May 2009
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    71

    is this convergent?

    inf (x ^ 2) + 1
    sum -----------------
    x=1 3 x ^ 3 - x + 2

    I find potentially convergent

    Then I say discard all but x ^2 / x^3, so that simplifies to be:
    1/x

    use p series test ast 1/x = 1/x^1, where the 1 is <=1 and hence divergent.

    x ^ 2 + 1
    ---------------
    3 x^ 2 -x + 2

    -----------------
    1/x

    = ... lim
    x->inf x(x^2+1)
    ----------
    3x^2-x+2

    = inf which is > 1

    so the answer is... this is divergent by limit comparison test.
    Is that right?
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  2. #2
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    Quote Originally Posted by orendacl View Post
    inf (x ^ 2) + 1
    sum -----------------
    x=1 3 x ^ 3 - x + 2

    I find potentially convergent


    If you meant to write the series \sum^\infty_{n=1}\frac{n^2+1}{3n^3-n+2} , then you have a divergent series using, for example, the comparison test: \frac{n^2+1}{3n^3-n+2}\geq \frac{n^2}{4n^3}=\frac{1}{4n} , and

    since the last one is the general term of a multiple of the harmonic series' general term then it diverges.

    Tonio


    Then I say discard all but x ^2 / x^3, so that simplifies to be:
    1/x

    use p series test ast 1/x = 1/x^1, where the 1 is <=1 and hence divergent.

    x ^ 2 + 1
    ---------------
    3 x^ 2 -x + 2

    -----------------
    1/x
    = ... lim
    x->inf x(x^2+1)
    ----------
    3x^2-x+2

    = inf which is > 1

    so the answer is... this is divergent by limit comparison test.
    Is that right?
    .
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