Series of Primes

  • Thread starter Dragonfall
  • Start date
  • #1
1,030
4
Erdos noticed that [tex]\sum(-1)^n\frac{n\log n}{p_n}[/tex] diverges, where pn is the nth prime. I can't prove this conclusively. All I can say is that PNT implies that p_n~nlogn and thus the series "resembles" [tex]\sum(-1)^n[/tex].
 

Answers and Replies

  • #2
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,916
19
If the terms don't go to zero, then the sum doesn't converge, right?
 
  • #3
1,030
4
Oh ya, how the hell did I miss that?
 

Related Threads on Series of Primes

  • Last Post
Replies
2
Views
2K
Replies
1
Views
2K
  • Last Post
Replies
8
Views
3K
  • Last Post
2
Replies
38
Views
5K
  • Last Post
Replies
10
Views
3K
  • Last Post
Replies
9
Views
3K
Replies
3
Views
3K
Replies
9
Views
4K
Replies
8
Views
4K
Top