- #1
B18
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Homework Statement
Determine whether the series is convergent or divergent by expressing s sub n as a telescoping series. If convergent find the sum.
[tex] \sum_{n=2}^\infty \frac{1}{n^3-1} [/tex]
The Attempt at a Solution
First thing I did was partial fraction decomposition.
Resulting in: Ʃ (n=2 to ∞) (-1/n+(1/2)/(n+1)+(1/2)/(n-1))
What I am confused with is when I try to find the partial sum nothing is canceling out. I tried to making it into this: Ʃ(n=2 to ∞) -1/n+(1/2)*Ʃ(n=2 to ∞) (1/n-1)+(1/n+1) but this didn't click with me either.
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