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: 6,379 Thanks: 542 
I don't know if this would satisfy you. However for large n, $\displaystyle a_n \approx \frac{1}{2n}$.


Tags 
convergence, series 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Convergence and Series Sum  Luiz  Real Analysis  1  May 10th, 2015 10:38 AM 
Series Convergence  Kreiger  Real Analysis  5  April 19th, 2015 04:09 PM 
Sum of series and convergence  Luiz  Real Analysis  1  March 22nd, 2015 02:22 PM 
Another Series Convergence  HairOnABiscuit  Real Analysis  1  April 28th, 2010 12:41 AM 
series convergence  mrjones  Real Analysis  12  April 9th, 2010 08:38 AM 