Series convergence

  • Thread starter photis
  • Start date
  • #1
7
0
It's easy to see that [tex]\sum_{n=2}^{\infty}\frac{1}{lnn}[/tex] does not converge. But what happens to [tex]\sum_{n=2}^{\infty}\frac{1}{(lnn)^k}[/tex] with k > 1 and why?

Can anybody help?
 

Answers and Replies

  • #2
176
0
i'm pretty sure it diverges for all k>1. this is because n/((lnn)^k) goes to infinity for all integer values of k. THink about this - use L'Hopitals rule and definition of a limit for a formal proof using the comparison test with the harmonic series.
 
  • #3
7
0
Thanks!
 

Related Threads on Series convergence

  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
15
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
2
Views
633
  • Last Post
Replies
15
Views
3K
  • Last Post
Replies
9
Views
2K
  • Last Post
Replies
10
Views
2K
Top