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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

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

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