Does the following sequence converge or diverge? If it converges then find the limit. An = ln(n) / ln(n+1).

Question

Does the following sequence converge or diverge?  If it converges then find the limit.  An = ln(n) / ln(n+1).

turingtest · Answer

do you know l'Hospital's rule yet?

anonymous · Answer

yes

anonymous · Answer

taking the limit gives 0/0 so divergence test doesnt work

turingtest · Answer

what is the derivative of the numerator?
what is the derivative of the denominator?

anonymous · Answer

derivative of ln(n) = 1/n  and derivative of ln(n+1) = 1/(n+1)

anonymous · Answer

so if I take the limit of both they go to 0 right?

anonymous · Answer

wait this is a sequence so I don't use any of the tests

anonymous · Answer

so the sequence converges to 0?

turingtest · Answer

they don't to zero, one is in the denominator

turingtest · Answer

$${\frac d{dn}\ln n\over\frac d{dn}\ln(n+1)}=?$$

anonymous · Answer

ohh right I didnt flip the denominator x.x  so it's n+1/n which means it diverges to infinity.

turingtest · Answer

that does not diverge