Could anyone help me out with this equation please?

How to prove it? Any ideas?

Printable View

- January 15th 2013, 08:36 AMLisa91Series equation
Could anyone help me out with this equation please?

How to prove it? Any ideas? - January 15th 2013, 08:47 AMTheSaviourRe: Series equation
Yes consider the partial fraction expansion of .

Two of the fractions will telescope and you'll be done.

P.S. join mathhelpboards.com - this one is done for. ;) - January 15th 2013, 09:31 AMLisa91Re: Series equation
Could you write it out please? You mean ?

- January 15th 2013, 09:47 AMILikeSerenaRe: Series equation
Yes, try to write it as

Deduce what A, B, and C are.

Do you know how to?

Then split the summation into 3 summations. - January 15th 2013, 09:58 AMLisa91Re: Series equation
OK, I did it. . Is it ok?

- January 15th 2013, 10:00 AMTheSaviourRe: Series equation
- January 15th 2013, 10:03 AMLisa91Re: Series equation
So, I got something like this: I still don't see what I can take out of this...

- January 15th 2013, 10:06 AMILikeSerenaRe: Series equation
You have a summation that starts at n=2.

Rewrite the summation of the second term by replacing n-1 by for instance k.

And rewrite the summation of the third term by replacing n+1 by m.

Afterward add or subtract whatever you need to, to make the summations start at 1.

Then you can combine them again. - January 15th 2013, 10:09 AMLisa91Re: Series equation
Oh sorry stupid question.

- January 15th 2013, 10:12 AMTheSaviourRe: Series equation
- January 15th 2013, 10:13 AMILikeSerenaRe: Series equation
You can split the summation into 3 summations.

The second summation is:

Substitute n=k+1 and you'll get:

- January 15th 2013, 10:23 AMLisa91Re: Series equation
The third term is . How can I 'go back' to 1?

- January 15th 2013, 10:33 AMTheSaviourRe: Series equation
By subtracting the terms at m = 2, and m = 1.

- January 15th 2013, 10:41 AMLisa91Re: Series equation
So, I got How to combine them all? I don't know how to cope with those . For instance, if I go back to n, I get n=0 in the first term, which is not what I want...

- January 15th 2013, 10:51 AMTheSaviourRe: Series equation
3S+S/3-2S Surely you can combine that. :D

Make all indexes k if that's confusing you.