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March 30th, 2018, 08:50 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, 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 $(k + 1) * k^k \le (k + 1)^{(k + 1)} = (k + 1) * (k + 1)^k \text { if } k \ge 1.$ 

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induction, mathematical, prove 
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