Series Proofs

  • Thread starter prace
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  • #1
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Homework Statement


The question asked was to "Show that..." with regards to the equations stated below.


Homework Equations



http://album6.snapandshare.com/3936/45466/862870.jpg [Broken]

sorry for such a large image... I am not too savvy with the latex yet, so i just linked an image that i created with microsoft word.

The Attempt at a Solution



So, I know I am suppossed to show an attempt at this solution, but I am completely boggled on where to even start. One thing I did try to do for the first equation was to just substitute in values for n starting at 2. This did not really do much for me because as I continued along, the equation just came out to be ln(1-(some number smaller and smaller than 1)).

The only thing I can take out of the second equation is that the series will converge at pi, but I don't see how that is going to help me. I also tried substitute in numbers for n but again, no help there. I did find out however that the series was an alternating series, but I guess that was pretty obvious from the original statement of the problem.

Any help with getting me started with this would be greatly appreciated!!
 
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Answers and Replies

  • #2
benorin
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Hint [tex]\sum_k \ln a_k = \ln\prod_k a_k[/tex]
 
  • #3
1,074
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The first series should probably start at 2, but it can not start at 1 because it it does than it is undefined.
 
  • #4
102
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Hint [tex]\sum_k \ln a_k = \ln\prod_k a_k[/tex]

Hi,

Thanks for the responses. Sorry for the dumb question, but what does the symbol in the right hand side of the equation after the ln mean? I don't think I have seen that one before. :confused: thanks.
 
  • #5
1,074
1
Hi,

Thanks for the responses. Sorry for the dumb question, but what does the symbol in the right hand side of the equation after the ln mean? I don't think I have seen that one before. :confused: thanks.


It's an infinite product.
 
  • #6
102
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cool thanks, I am going to try and figure it out! I'll be back =)
 

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