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Requiem
 2 years ago
Determine convergence or divergence.
(1)^n/(n^3)
I know that I want to use the alternating series test. I used (bsubn) as 1/n^3 and (bsubn+1) as 1/(n+1)^3. I know that (bsubn) as n > infinity equals 0, but is (bsubn+1) less than or equal to (bsubn)?
Requiem
 2 years ago
Determine convergence or divergence. (1)^n/(n^3) I know that I want to use the alternating series test. I used (bsubn) as 1/n^3 and (bsubn+1) as 1/(n+1)^3. I know that (bsubn) as n > infinity equals 0, but is (bsubn+1) less than or equal to (bsubn)?

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Requiem
 2 years ago
Best ResponseYou've already chosen the best response.0Or do i need to use a comparison test?

Requiem
 2 years ago
Best ResponseYou've already chosen the best response.0I know that those two conditions have to be met for it to be convergent...

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0is it \[\sum_{n=1}^{\infty}\frac{(1)^n}{n^3}\]

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0it not only converges, but it converges absolutely

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0all you need for the alternating series to converge is that the terms go to zero, which thsee certainly do

Requiem
 2 years ago
Best ResponseYou've already chosen the best response.0oh ok..in my book it says that (bsubn+1) has to be less than or equal to (bsubn) but also that (bsubn) has to equal 0 when the limit is taken...

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0but \[\sum_{n=1}^{\infty}\frac{1}{n^3}\] also converges, so this series is not just convergent, it is absolutely convergent as well

Requiem
 2 years ago
Best ResponseYou've already chosen the best response.0and i wasnt sure if the former was true

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0yeah only need the terms go to zero

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0\[\sum\frac{(1)^n}{n}\] for example converges, although not absolutely

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0hell, even \[\sum\frac{(1)^n}{\ln(n)}\] converges

Requiem
 2 years ago
Best ResponseYou've already chosen the best response.0its converges conditionally right?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0the last two i wrote are only conditionally convergent, the one you posted is absolutely convergent, a stronger condition

Requiem
 2 years ago
Best ResponseYou've already chosen the best response.0ok thanks you for your help! much appreciated
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