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Homework Help: Does this sequence converge?

  1. Oct 5, 2013 #1
    I have to examine whether this sequence

    Xn = ln(n^2+1) - ln(n)

    converges or diverges.

    My attempt at a solution:

    Xn = ln(n^2+1) - ln(n) = ln((n^2+1)/n) = ln(n+1/n)

    Xn → ∞ when n → ∞

    So the sequence diverges.

    Can someone look at this and see whether the procedure and conclusion is right or wrong ?

    Thank you.
  2. jcsd
  3. Oct 5, 2013 #2


    User Avatar
    2017 Award

    Staff: Mentor

    That is good. I would probably add a final step ln(n+1/n) > ln(n).
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