August 12th, 2019, 05:46 AM  #1 
Senior Member Joined: Dec 2015 From: somewhere Posts: 708 Thanks: 96  Solve inequality
For which values of N : $\displaystyle \; \sum_{j=1}^{N} j^{1} >\frac{N}{\ln(N+1)}$.
Last edited by idontknow; August 12th, 2019 at 05:51 AM. 
August 12th, 2019, 06:25 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 21,015 Thanks: 2250 
Do you know of any natural number for which that inequality doesn't hold?

August 12th, 2019, 08:39 AM  #3  
Senior Member Joined: Dec 2015 From: somewhere Posts: 708 Thanks: 96  Quote:
The right side is increasing for x>e and the rate of divergence is larger than the left side so $\displaystyle N\geq \lceil e \rceil =3$. If the left side is smaller than right side for N>2 then it is larger for N<3 .  
August 12th, 2019, 04:23 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 21,015 Thanks: 2250  

Tags 
inequality, solve 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Can't solve this inequality  antinutrient  Real Analysis  2  April 28th, 2015 06:29 PM 
solve inequality  brhum  Algebra  2  June 26th, 2014 05:35 PM 
Solve an inequality hence solve another inequality  Punch  Algebra  3  July 2nd, 2012 12:43 PM 
Solve the Inequality.  jattrockz  Algebra  5  November 10th, 2011 05:07 AM 
how to solve this inequality  sikwn32  Algebra  5  August 30th, 2009 02:12 PM 