I found that it diverges but now I must check for conditionally convergent, can I

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Liul

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only use alt.series test now? I have to state whether it's absolute convergence, conditional convergence, or divergence.
I learned that if I get the answer of divergent, then I must check for conditionally convergent.so,

Ex. I found SUM (-1)^(n+1) n!/2^n to = infinity which is Divergent by my test. So now I'm thinking I need to check for conditionally convergent but I do not know how to apply the alternating series test to n!/2^n to confirm that it does or doesn't conditionally converge

thank you
 
You need to use the absolute convergence ratio test first....

first get rid of the -1^(n+1) by taking the absolute value of the equation because it is now just positive 1.
then find the limit of Uk+1/Uk which is { f(n+1)/f(n) } and if the limit is less then one it converges absolutly, if it is greater then one it diverges absolutly (follow this with alt series test also to check for condition convergence) and if it equals one you need to do another test which would be the alternating series test. where you test for the first number being larger then the second in the series as well as that the limit equals zero.

NOTE: when doing the ratio test set (n+1)! equal to n!(n+1) and 2^(n+1) to 2^n(2)
 
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