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Math Help - Root Test

  1. #1
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    Root Test

    In this problem you must attempt to use the Root Test to decide whether the series converges

    f(n)=(5n+4)^n
    (n+9)^(2n)
    n from 1 to infinity

    Enter the numerical value of the limit L if it converges, INF if it diverges to infinity, MINF if it diverges to negative infinity, or DIV if it diverges but not to infinity or negative infinity.
    L=

    Which of the following statements is true?
    A. The Root Test says that the series converges absolutely.
    B. The Root Test says that the series diverges.
    C. The Root Test says that the series converges conditionally.
    D. The Root Test is inconclusive, but the series converges absolutely by another test or tests.
    E. The Root Test is inconclusive, but the series diverges by another test or tests.
    F. The Root Test is inconclusive, but the series converges conditionally by another test or tests.

    I'm pretty sure L=0 and part b is D however that answer is coming up incorrect
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  2. #2
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    Re: Root Test

    Quote Originally Posted by kjnabs View Post
    In this problem you must attempt to use the Root Test to decide whether the series converges
    f(n)=(5n+4)^n
    (n+9)^(2n)
    n from 1 to infinity
    Enter the numerical value of the limit L if it converges, INF if it diverges to infinity, MINF if it diverges to negative infinity, or DIV if it diverges but not to infinity or negative infinity.
    L= Which of the following statements is true?
    A. The Root Test says that the series converges absolutely.
    B. The Root Test says that the series diverges.
    C. The Root Test says that the series converges conditionally.
    D. The Root Test is inconclusive, but the series converges absolutely by another test or tests.
    E. The Root Test is inconclusive, but the series diverges by another test or tests.
    F. The Root Test is inconclusive, but the series converges conditionally by another test or tests.
    I'm pretty sure L=0 and part b is D however that answer is coming up incorrect
    @kjnabs;779634, If you want to get more out of this site you need to learn to use LaTeX coding.
    \sqrt[n]{{\left| {\frac{{{{\left( {5n + 4} \right)}^n}}}{{{{\left( {n + 9} \right)}^{2n}}}}} \right|}} = \frac{{5n + 4}}{{{n^2} + 18n + 81}} \to 0

    Therefore the answer is: A. The Root Test says that the series converges absolutely. .
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