Does this sequence converge?

  • Thread starter Tala.S
  • Start date
  • #1
43
0
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.
 

Answers and Replies

  • #2
35,389
11,734
That is good. I would probably add a final step ln(n+1/n) > ln(n).
 

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