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#1 Help Me ! » Unbounded sequence that doesnt diverge to -∞ or ∞ » 2007-02-12 08:59:58

woodoo
Replies: 5

I have a question that says find an unbounded sequence that doesn't diverge to -∞  or ∞. I can't figure one out, I don't think it exists. Anyone know of one?

#2 Help Me ! » Help with an approximation of Dirichlet's Test » 2007-02-12 05:51:33

woodoo
Replies: 0

As used in another thread I have this problem
e9f43435d0483405b36b2fcd062aaa1.gif

I am asked to find the value of n to approximate the series to the millionth place, then find that approximation. I am confused by this wording. Does anyone understand this and know how I should go about doing this? Thanks

#3 Help Me ! » Help with a series » 2007-02-12 05:40:41

woodoo
Replies: 2

I have this problem that I can't figure out.
                                                                                                                                                                         
a_n is a sequence of positive #s. For each n in the natural #s, b_n = (a1+a2+...+an)/n. And I have to use this to show


∑ b_n   
n=1     
                                                                                                                                                                   
diverges to positive infinity. Any1 have any ideas?

#4 Re: Help Me ! » I don't understand Dirichlet's Test » 2007-02-12 05:32:57

So if Zhylliolom right? Because you guys are confusing me

#5 Re: Help Me ! » I don't understand Dirichlet's Test » 2007-02-11 20:15:28

Oh I understand now, I thought that {bn} was going to have to equal (sin n)/n, I didn't realize you were supposed to break down (sin n)/n into {an} = 1/n and {bn} = sin n to represent

1e5a14e85c161d005de3ce4877f65d1.gif

Thank you Zhylliolom

#6 Help Me ! » I don't understand Dirichlet's Test » 2007-02-11 19:47:42

woodoo
Replies: 14

I can't grasp the concept of Dirichlet's Test,


I've looked online, but I don't understand it. Can someone give me a simple example to explain it.

Thanks

edit: I think what is confusing me is this:

img8.png

Am I supposed to prove that is true or do I just assume it is?

#7 Help Me ! » Converges or Diverges, did I do this right? » 2007-02-11 17:37:45

woodoo
Replies: 1

I have the problem which I must find convergent or divergent:

infinity           _____
    ∑        1/(√n^3-2)
  n= 2

I used the Comparison Test with a p-series to get that it's convergent. Is this correct?
       _____             ____
1/(√n^3-2)  <  1/(√n^3)   =  1/n^(3/2)  so it converges

#8 Re: Help Me ! » Help me make this converge » 2007-02-11 14:54:17

wow that was a lot easier than I thought, thank you

#9 Help Me ! » Help me make this converge » 2007-02-11 13:46:06

woodoo
Replies: 3

The problem I have wants me to prove the following statement false:

"If a_n and b_n are both divergent sequences then (a_n + b_n) diverges also."

I can't come up with a two divergent sequences that with converge if I add them together. Anyone have any ideas? Thanks

#10 Re: Help Me ! » Help with Dirichlet's test » 2007-02-11 11:15:59

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

#11 Help Me ! » Help with Dirichlet's test » 2007-02-10 21:55:10

woodoo
Replies: 4

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.

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