What is the sum of the following series:

SUMMATION(n=1 to infiniti) -1/(n^2 + 9n + 20)

I tried using the forumula:

sum = a/(1-r)

But i cant get an exact value for r so i am not sure

Thanks

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- May 21st 2008, 09:36 AMtaurusSum of series
What is the sum of the following series:

SUMMATION(n=1 to infiniti) -1/(n^2 + 9n + 20)

I tried using the forumula:

sum = a/(1-r)

But i cant get an exact value for r so i am not sure

Thanks - May 21st 2008, 09:43 AMcolby2152
- May 21st 2008, 09:43 AMMoo
- May 21st 2008, 10:03 AMtaurus
I still dont get it.

What happened to your first line with n-n etc?

Also i still dont get how to get the sum then? - May 21st 2008, 10:09 AMcolby2152
- May 21st 2008, 10:15 AMMoo
I grouped the terms..

For the sum, you can notice that each term is annulated by the one which follows, apart from the first term, -1/5.

Telescoping series - Wikipedia, the free encyclopedia - May 21st 2008, 10:17 AMtaurus
i cant conclude anything, all i see is a series of numbers with 1/7 repeated?

- May 21st 2008, 10:23 AMMoo
- May 21st 2008, 10:30 AMtaurus
but that doesnt give me the sum.

- May 21st 2008, 10:39 AMarbolisQuote:

Therefore, there remains only -1/5 at the end

- May 21st 2008, 10:48 AMtaurus
But when i enter that as an answer it says its wrong it says:

Your answer is not correct.

Hint: break up the summand as partial fractions and then write out the series to the first few terms. - May 21st 2008, 10:52 AMTheEmptySet
- May 21st 2008, 10:54 AMMoo
- May 21st 2008, 10:57 AMtaurus
oh sorry, this si totally my fault, typo

correct question is:

SUMMATION(n=1 to infiniti) -2/(n^2 + 9n + 20)

?

thanks - May 21st 2008, 10:58 AMMoo