November 3rd, 2019, 07:28 AM  #1 
Senior Member Joined: Dec 2015 From: Earth Posts: 823 Thanks: 113 Math Focus: Elementary Math  Range of X
Find the range of X such that $\displaystyle (X+6)^{n} \cdot n!\geq n^n \; , n\in \mathbb{N} ,X\in \mathbb{R}.$ 
November 3rd, 2019, 07:59 AM  #2 
Member Joined: May 2013 Posts: 57 Thanks: 5 
unfortunately there's no definitive answer to this question as you have two variables rather than 1. setting n=2 will give a different range for x than setting it to 9. 
November 3rd, 2019, 08:32 AM  #3 
Senior Member Joined: Sep 2015 From: USA Posts: 2,638 Thanks: 1473  he's looking for the infinite intersection of all ranges of X over all the natural numbers.

November 3rd, 2019, 09:48 AM  #4 
Senior Member Joined: Mar 2015 From: Universe 2.71828i3.14159 Posts: 169 Thanks: 65 Math Focus: Area of Circle  

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