My Math Forum  

Go Back   My Math Forum > High School Math Forum > Elementary Math

Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion


Thanks Tree2Thanks
  • 2 Post By mathman
Reply
 
LinkBack Thread Tools Display Modes
November 29th, 2017, 09:03 AM   #1
Senior Member
 
Joined: Dec 2015
From: Earth

Posts: 181
Thanks: 23

Another factorial inequality

Prove that $\displaystyle n!^2 \geq n^n$ for $\displaystyle n\in N$
idontknow is offline  
 
November 29th, 2017, 02:45 PM   #2
Global Moderator
 
Joined: May 2007

Posts: 6,397
Thanks: 546

Mathematical induction can work. For n=1 or 2, equality. For n=3, 36 > 27.

In general. $(n+1)!^2=(n+1)^2(n!)^2$
$(n+1)^{n+1}=(n+1)n^n(1+\frac{1}{n})^n<(n+1)n^ne<( n+1)^2(n!)^2$, for n > 2.
Thanks from greg1313 and Country Boy
mathman is offline  
Reply

  My Math Forum > High School Math Forum > Elementary Math

Tags
factorial, inequality



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
factorial tahir.iman Algebra 9 December 26th, 2012 07:22 PM
Inequality with e, factorial, exponential function... annakar Algebra 2 December 9th, 2012 02:31 AM
Factorial bilano99 Calculus 2 May 1st, 2012 11:12 AM
n! (factorial) thomasthomas Number Theory 13 November 6th, 2010 07:21 AM
factorial q coolaid317 Calculus 8 April 28th, 2010 07:21 PM





Copyright © 2017 My Math Forum. All rights reserved.