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Math Help - Mathematical induction

  1. #1
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    Unhappy Mathematical induction

    I am new to mathematical induction and just do not get it at all. I have been working on 5^n < (n+2)! for n>=4 for about 3 hours now. I just do not understand what to do after the k+1 portion of the proof. Any help would GREATLY appreciated.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Mathematical induction

    Quote Originally Posted by jls7168 View Post
    I am new to mathematical induction and just do not get it at all. I have been working on 5^n < (n+2)! for n>=4 for about 3 hours now. I just do not understand what to do after the k+1 portion of the proof. Any help would GREATLY appreciated.
    5^k\leq (k+2)!\Rightarrow  5^{k+1}\leq 5(k+2)!\Rightarrow \;(\textrm{\;as\;}k\geq 4)\;5^{k+1}\leq (k+3)[(k+2)!]=(k+3)!
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