# Series Proofs

## 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!!

Last edited by a moderator:

benorin
Homework Helper
Hint $$\sum_k \ln a_k = \ln\prod_k a_k$$

The first series should probably start at 2, but it can not start at 1 because it it does than it is undefined.

Hint $$\sum_k \ln a_k = \ln\prod_k a_k$$

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. thanks.

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. thanks.

It's an infinite product.

cool thanks, I am going to try and figure it out! I'll be back =)