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Math Help - Ratio test help -simple Question

  1. #1
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    Ratio test help -simple Question

    For the ratio test:

    Is (2n-1) + 1 = 2n?

    I have to use the ratio test to evaluate n2/(2n-1)! where n=1 for an infinite series...exam in a few hrs!
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  2. #2
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    Quote Originally Posted by Joanna Jakma View Post
    For the ratio test:

    Is (2n-1) + 1 = 2n?
    yes...this should be simple algebra for someone dealing with series. and what does this have to do with the ratio test?

    I have to use the ratio test to evaluate n2/(2n-1)! where n=1 for an infinite series...exam in a few hrs!
    do you mean \frac {n^2}{(2n - 1)!}?

    if so, we want to see if \lim \left| \frac {\frac {(n + 1)^2}{(2n + 1)!}}{\frac {n^2}{(2n - 1)!}} \right| = \lim \left| \frac {(n + 1)^2}{n^2} \cdot \frac {(2n - 1)!}{(2n + 1)!} \right|< 1

    if so, the series \sum \frac {n^2}{(2n - 1)!} converges absolutely

    by the way, what you wanted was 2(n + 1) - 1 = 2n + 1, not what you said before
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  3. #3
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    CHeers for that!

    Yes you got it right.
    But surely
    (2n-1)+1 = 2n? as opposed to 2n+1?

    So when doing the ratio test should it not be 2n! as opposed to (2n+1)! in that equation? I'm confused
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  4. #4
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    Quote Originally Posted by Joanna Jakma View Post
    CHeers for that!

    Yes you got it right.
    But surely
    (2n-1)+1 = 2n? as opposed to 2n+1?
    Yes, (2n-1)+1 = 2n. But that's NOT what Jhevon wrote at the end their post. Jhevon pointed out that

    2(n + 1) - 1

    is what you should have. And 2(n + 1) - 1 = 2n + 1.

    2(n + 1) - 1 is NOT (2n-1)+1.
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