January 4th, 2012, 06:47 PM  #1 
Senior Member Joined: Jul 2011 Posts: 405 Thanks: 16  limit 
January 4th, 2012, 07:19 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond  Re: limit
1. After an application of L'Hopital's rule the limit is found to be 0. 
January 4th, 2012, 09:06 PM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: limit
2.) We see that the numerator diverges, so we have the indeterminate form ?/?, so applying L'Hôpitals rule (using differencing rather than differentiation, since n is discrete, rather than continuous): We have the indeterminate form ?/?, so applying L'Hôpitals rule: Converting from logarithmic to exponential form: 
January 4th, 2012, 11:36 PM  #4 
Senior Member Joined: Jul 2011 Posts: 405 Thanks: 16  Re: limit
Thanks Markfl and Greg

January 4th, 2012, 11:48 PM  #5 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: limit
Would you humor me and demonstrate that what Greg posted is correct? Greg knows it's correct and I know it's correct...but can you demonstrate how to arrive at the given conclusion? I'm not trying to be contrary, rather I want to make sure you understand how it works...for your benefit. 
January 5th, 2012, 08:20 AM  #6 
Senior Member Joined: Jul 2011 Posts: 405 Thanks: 16  Re: limit
actually Markfl I have got it Which is Using The formula When then and Markfl your explanation is crystal clear. so I have got your explanation. thanking you 
January 5th, 2012, 04:35 PM  #7 
Senior Member Joined: Dec 2011 From: Argentina Posts: 216 Thanks: 0  Re: limit
I guess this is a long shot but consider this: Let's put the sum this way: Now for And for 

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