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# Determine whether the sequence converges or diverges. If it converges, find the limit.$\left \{ \frac {\ln n}{\ln 2n} \right \}$

## The sequence Converges to 1

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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### Video Transcript

for this problem. We're looking at a n equals natural log of n divided by natural log of two in So one thing you, Khun Dio, when you're looking at the limit as in goes to infinity is you could apply low petals rule to this Another thing that you could do It would be to write this as natural log of n divided by natural log of in plus natural log of two. Hello. Patel's rule would work fun, rewriting and in this way would also work well. And now when you do limit as n goes to infinity of Anne, you could do it. But I do know Patel's rule or written in this way we could also do the trick where we look at the term that's going to infinity, the fastest and the denominator, and divide the top on the bottom by that term so we can divide the top on the bottom by natural log in. And as n goes to infinity, this term is going to go to zero. We just have one over one, which is one. So the sequence does converge. It converges to one

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp