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        riddles >> putnam exam (pure math) >> Convergent or Divergent?
        
(Message started by: ThudanBlunder on Nov 26^th, 2008, 8:31am)

Title: Convergent or Divergent?
Post by ThudanBlunder on Nov 26^th, 2008, 8:31am

http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/infty.gif
http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/sum.gif(nlogn.loglogn)^-1
n=3

Title: Re: Convergent or Divergent?
Post by Obob on Dec 1^st, 2008, 9:29pm

[hide]Integral test.[/hide]

Title: Re: Convergent or Divergent?
Post by ThudanBlunder on Dec 4^th, 2008, 3:49pm

on 12/01/08 at 21:29:31, Obob wrote:

[hide]Integral test.[/hide]

Ah yes, I hadn't realized that the integral of the given function is logloglogx. ::)

Perhaps I should have asked how many terms are required for the sum to exceed 10.

Title: Re: Convergent or Divergent?
Post by ThudanBlunder on Dec 15^th, 2008, 7:21pm

on 12/04/08 at 15:49:58, ThudanBlunder wrote:

Perhaps I should have asked how many terms are required for the sum to exceed 10.

Let N = Number of terms required for function to exceed 10

F(n): 1/loglog(n) for n > 2
N: 1

F(n): 1/log(n) for n > 1
N: 20

F(n): 1/http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gifn for n > 0
N: 33

F(n): 1/n for n > 0
N: 12367

F(n): 1/nlog(n) for n > 1
N: 10⁴³⁰⁰

F(n): 1/[nlog(n)*loglog(n)] for n > 2
N: googolplex