Finding the limit of lim_(n->oo) (n^(log(n)))/((log n)^n)

Siena Erickson

Siena Erickson

Answered question

2022-11-13

Finding the limit of lim n n l o g ( n ) ( log n ) n
I try to calculate the following limit:
lim n n log ( n ) ( log n ) n
I tried this:
lim n e ( log ( n ) ) 2 n log ( log ( n ) )
Is this useful? & what do now?

Answer & Explanation

avuglantsaew

avuglantsaew

Beginner2022-11-14Added 15 answers

It is useful. Now, you could try to look at log 2 n n log log n and see if it converges or diverges to ± -- any of the two will give you the limit you're looking for.
As a start, rewrite
log 2 n n log log n = n ( log 2 n n log log n )
In the parenthesis, the second term goes to . What about the first?

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?