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Math Help - Sequence Convergence question

  1. #1
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    Sequence Convergence question

    Determine if the sequence {(2n-1)/(3n^2+1)} n=1,2,3.... converges or diverges. If the sequence converges find its limit.

    I did L'Hopital's rule to find the limit which I found to be 2/infinity= 0. Is this correct? Would that mean that the sequence converges. Would this also mean that the limit is 0?

    Thanks in advance.
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  2. #2
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    Quote Originally Posted by ihatemath View Post
    Determine if the sequence {(2n-1)/(3n^2+1)} n=1,2,3.... converges or diverges. If the sequence converges find its limit.

    I did L'Hopital's rule to find the limit which I found to be 2/infinity= 0. Is this correct? Would that mean that the sequence converges. Would this also mean that the limit is 0?

    Thanks in advance.
    yes, since ...

    \displaystyle \lim_{n \to \infty} \frac{2n-1}{3n^2+1} = 0

    ... the sequence converges to 0.
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