March 30th, 2017, 01:28 AM  #1 
Senior Member Joined: Jul 2011 Posts: 400 Thanks: 15  series sum
Evaluation of $\displaystyle \lim_{n\rightarrow \infty}\sum^{n}_{k=1}\frac{1}{(k1)\sqrt{k}+k\sqrt{k+1}}$

March 30th, 2017, 06:25 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,806 Thanks: 1045 Math Focus: Elementary mathematics and beyond 
Are you sure it's typed correctly? The summand is undefined at k = 1.

March 31st, 2017, 02:23 AM  #3  
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,102 Thanks: 703 Math Focus: Physics, mathematical modelling, numerical and computational solutions  Quote:
As for the evaluation of the summand for all k? Hmmm.... Last edited by Benit13; March 31st, 2017 at 03:02 AM.  
April 6th, 2017, 08:21 PM  #4 
Senior Member Joined: Jul 2011 Posts: 400 Thanks: 15  
April 7th, 2017, 01:08 AM  #5 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,102 Thanks: 703 Math Focus: Physics, mathematical modelling, numerical and computational solutions  
April 8th, 2017, 04:15 AM  #6 
Senior Member Joined: Jul 2011 Posts: 400 Thanks: 15  
April 8th, 2017, 08:11 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 18,956 Thanks: 1603 
Big hint: $\dfrac{1}{(k1)\sqrt{k}+k\sqrt{k1}} = \dfrac{1}{\sqrt{k1}}  \dfrac{1}{\sqrt{k}}$.


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