My Math Forum  

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

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
March 30th, 2018, 08:50 PM   #1
Senior Member
 
Chikis's Avatar
 
Joined: Jan 2012

Posts: 745
Thanks: 7

Prove using mathematical induction

Hello everybody. Please I need your help. I was ask to prove that n! <= n^n¥ positive integer using mathematical induction. I couldn't do it. Please I need your help.

Just a bit interpretation: <= means greater or equal to. n^¥ means n raised to the power of v with crossed. I know the forum has better ways of writing these symbols. I just that time would allow me to find it out. Please understand with me. Thank you.
Chikis is offline  
 
March 31st, 2018, 08:38 AM   #2
Senior Member
 
Joined: May 2016
From: USA

Posts: 1,310
Thanks: 552

Does this hint help?

Can you show that

$(k + 1) * k! \le (k + 1) * k^k \text { if } k! \le k^k \text { and } k \ge 1.$

Can you show that

$(k + 1) * k^k \le (k + 1)^{(k + 1)} = (k + 1) * (k + 1)^k \text { if } k \ge 1.$
JeffM1 is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
induction, mathematical, prove



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Mathematical Induction: Prove that n^2 < 2^n then n > 4 DecoratorFawn82 Algebra 4 October 7th, 2017 04:26 AM
how to prove this without mathematical induction numeriprimi Elementary Math 2 September 30th, 2017 12:28 PM
Prove using mathematical induction wannabemathlete Algebra 4 October 23rd, 2014 11:01 PM
How to prove this by mathematical induction? hs_pec Algebra 1 January 16th, 2013 07:28 PM
Prove with mathematical induction Phatossi Algebra 4 November 10th, 2012 06:27 PM





Copyright © 2019 My Math Forum. All rights reserved.