Does the sequence ln(n²+1) − ln(n) converge?

[Tala.S]

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.

 

[mfb]

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