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Math Help - Limits question

  1. #1
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    Limits question

    (2n+1)n!/(n+1)!.. I know that is the same as (2n+1)/(n+1).. how do i prove this is convergent and how do i find the limit?
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  2. #2
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    Quote Originally Posted by calculuskid1 View Post
    (2n+1)n!/(n+1)!.. I know that is the same as (2n+1)/(n+1).. how do i prove this is convergent and how do i find the limit?
    Is this a sequence or a series?
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    it is a sequence
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    \frac{2n + 1}{n + 1} = \frac{2n + 2}{n + 1} - \frac{1}{n + 1}

     = \frac{2(n + 1)}{n + 1} - \frac{1}{n + 1}

     = 2 - \frac{1}{n + 1}.


    What happens as n \to \infty?
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  5. #5
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    Quote Originally Posted by Prove It View Post
    \frac{2n + 1}{n + 1} = \frac{2n + 2}{n + 1} - \frac{1}{n + 1}

     = \frac{2(n + 1)}{n + 1} - \frac{1}{n + 1}

     = 2 - \frac{1}{n + 1}.


    What happens as n \to \infty?
    That is actually pretty elegant. Simple, too. Nice work.
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