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Math Help - Ratio Test

  1. #1
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    Ratio Test

    Can someone help me with the this ratio test. I am having problems canceling things and taking the limit.

    Use the ratio test to determine convergence or divergence or that the Ratio Test is inconclusive.



    Thanks
    AC
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  2. #2
    Junior Member rubix's Avatar
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    Ratio test - Wikipedia, the free encyclopedia

    see the formula

    a_n is what you have a_(n+1) is what you get by adding 1 i.e. ((n+1)^50)/(n+1)!

    noteworthy: (n+1)! = n! * (n+1)

    divide it out, play with it a bit, and see if you can get something out of it.
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  3. #3
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    Ok I understand how to to use the ratio test I would get the lim(|(n+1)^50/(n+1)!|*|n!/n^50|) I get it down to lim(|(n+1)^50/((n+1)*n^50)|) but Im not sure how to make it work from here . . .
    thanks
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  4. #4
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    Quote Originally Posted by Casas4 View Post
    Ok I understand how to to use the ratio test I would get the lim(|(n+1)^50/(n+1)!|*|n!/n^50|) I get it down to lim(|(n+1)^50/((n+1)*n^50)|) but Im not sure how to make it work from here . . .
    thanks
    Use the Binomial expansion on the numerator, then divide each term in the numerator and denominator by the highest power of n.
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  5. #5
    Ted
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    Another way for the limit:

    \frac{(n+1)^{50}}{(n+1) \, n^{50}}

    =\left( \frac{n+1}{n} \right)^{50} \cdot \frac{1}{n+1}

    =\left( 1+\frac{1}{n} \right)^{50} \cdot \frac{1}{n+1}

    =(1)^{50} \cdot (0)=0 as n goes to infinity

    since 0<1 ---> The series converges by the Ratio Test.
    PS: There is no need for the absolute values since n>1 here.
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