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March 30th, 2018, 08:50 PM   #1
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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.
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March 31st, 2018, 08:38 AM   #2
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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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