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Old July 4th, 2009, 11:29 AM
putnam120 putnam120 is offline
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Just thought I should mention that if \lim n^\alpha a_n=L with L\neq{0}.
Then \sum a_n<\infty if \alpha>1 and \sum a_n diverges if 0<\alpha\le{1}. Both of these shouldn't be too hard to prove. You basically use the comparison test idea shown in halbard's post.


I haven't looked at the cases where \alpha<0 yet.
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