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anonymous
 5 years ago
how do you determine if a series is absolutely ,conditionally convergent or divergent for a problem like this sigma (1)^n/2^n
anonymous
 5 years ago
how do you determine if a series is absolutely ,conditionally convergent or divergent for a problem like this sigma (1)^n/2^n

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watchmath
 5 years ago
Best ResponseYou've already chosen the best response.0The absolute series is a geometric series with ratio 1/2. Hence it is absolute convergent.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how would you test if it is conditionally convergent

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0since terms go to zero and it alternates it is conditionally convergent.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0would you use the latenating test along with another test?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I believe that this is an alternating series, and is convergent. its absolutely convergent if its still convergent using (1)^b/2^n with absolute value operator otherwise its conditionally convergent

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if it alternates, which this does because of the \[(1)^n\] then all you need for conditional convergence is that the terms go to zero.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay so you use the alternating test along with another test to see is it is absolutely or conditionally

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0to show absolute convergence you just check \[\sum\frac{1}{2^n}\] which as watchmath said, is a geometric series with \[r=\frac{1}{2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok i sense it is not clear from your question. absolute convergence is stronger than conditional. it is converges absolutely then it certainly converges conditionally

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0for an alternating series all you have to check for conditional convergence is that the terms go to zero.

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.0This is an example of series that conditionally convergent \(\sum (1)^n\frac{1}{n}\) The absolute value series is divergent since it is a harmonic series. But the original series is convergent by alternating series test. So it is always better to check it for the absolute series first.
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