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#1 2007-02-10 21:55:10

woodoo
Member
Registered: 2007-02-10
Posts: 11

Help with Dirichlet's test

I need to use Dirichlet's test to show

infinity
∑  (sin(n))/n        converges
n=1

Would 1/n work for bn? And how shall I go about solving this.

Last edited by woodoo (2007-02-10 21:55:43)

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#2 2007-02-11 03:52:18

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Help with Dirichlet's test

You want a_n = 1/n, if you go by the variable names on Wikipedia.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#3 2007-02-11 11:15:59

woodoo
Member
Registered: 2007-02-10
Posts: 11

Re: Help with Dirichlet's test

Are you sure an isn't (sin(n))/n ?

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#4 2007-02-11 14:47:36

George,Y
Member
Registered: 2006-03-12
Posts: 1,379

Re: Help with Dirichlet's test


∑(1/n) does not
1


X'(y-Xβ)=0

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#5 2007-02-11 18:24:31

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Help with Dirichlet's test

You want a_n to be a monotonely decreasing function bounded below by 0.  You want b_n to be bounded.  1/n fits the requirements for a, sin(n) fits the requirements for b.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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