My Math Forum Series convergence

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 May 28th, 2015, 07:56 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, 02:13 PM #2 Global Moderator   Joined: May 2007 Posts: 6,435 Thanks: 562 I don't know if this would satisfy you. However for large n, $\displaystyle |a_n| \approx \frac{1}{2n}$.

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