- #1
qeteshchl
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My apologies beforehand for not using the right format for this post.
Find the sum of (from 1 to inf) of [tex]\sum[/tex]8/(n(n+1)(n+2))
I approached the problem like I would a telescoping series by using partial faction decomposition to split it up. I arrived at:
[tex]\sum[/tex]4/n - 8/(n+1) + 4/(n+2)
I started plugging in numbers for 1 to try and arrive at a pattern:
(1 - 1 + 1/3) + (1/2 - 2/3 + 1/4) + (1/3 - 2/4 + 1/5) + (1/4 - 2/5 + 1/6) ...
I'm not seeing any discernible pattern to what is canceling out. Am I just approaching this problem wrong? Thanks for any help you guys may provide!
Homework Statement
Find the sum of (from 1 to inf) of [tex]\sum[/tex]8/(n(n+1)(n+2))
Homework Equations
The Attempt at a Solution
I approached the problem like I would a telescoping series by using partial faction decomposition to split it up. I arrived at:
[tex]\sum[/tex]4/n - 8/(n+1) + 4/(n+2)
I started plugging in numbers for 1 to try and arrive at a pattern:
(1 - 1 + 1/3) + (1/2 - 2/3 + 1/4) + (1/3 - 2/4 + 1/5) + (1/4 - 2/5 + 1/6) ...
I'm not seeing any discernible pattern to what is canceling out. Am I just approaching this problem wrong? Thanks for any help you guys may provide!