May 28th, 2015, 06:56 AM  #1 
Newbie Joined: May 2015 From: Prague Posts: 1 Thanks: 0  Series convergence
Hi, I would appreciate a little help with saying something about convergence of the following series (sorry for not using LaTeX): a_n=((1)^n)(e^(1/n)1)((n^2+4)^(1/2)(n^2+n)^(1/2)). I have found it is not going to converge absolutely (comparing with 1/n). Next I used criterion of Leibniz (I dont know the proper name of this criterion or rule). So lim(n>inf)(abs(a_n))=0 but I have problem with proving that for every integer a_n >= a_(n+1). Thank you in advance for help or showing me a way how to continue. PS: Sorry for bad english 
May 28th, 2015, 01:13 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,305 Thanks: 525 
I don't know if this would satisfy you. However for large n, $\displaystyle a_n \approx \frac{1}{2n}$.


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convergence, series 
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