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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.