
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
March 30th, 2018, 07:50 PM  #1 
Senior Member 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. 
March 31st, 2018, 07:38 AM  #2 
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551 
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 $(k + 1) * k^k \le (k + 1)^{(k + 1)} = (k + 1) * (k + 1)^k \text { if } k \ge 1.$ 

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 03:26 AM 
how to prove this without mathematical induction  numeriprimi  Elementary Math  2  September 30th, 2017 11:28 AM 
Prove using mathematical induction  wannabemathlete  Algebra  4  October 23rd, 2014 10:01 PM 
How to prove this by mathematical induction?  hs_pec  Algebra  1  January 16th, 2013 06:28 PM 
Prove with mathematical induction  Phatossi  Algebra  4  November 10th, 2012 05:27 PM 