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Math Help - how do you prove this using induction

  1. #1
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    how do you prove this using induction

    how do you prove this using induction-ggg.png

    can you help me with this question
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  2. #2
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    Re: how do you prove this using induction

    That looks pretty straight forward to me. Obviously when n= 0 or 1, f(0)= 0< 1= 5^0 and f(1)= 1< 5= 5^1.

    Now, suppose that f(k)< 5^k for all k< n. Then f(n+1)= 3f(n)+ 10f(n-1)< 3(5^n)+ 10(5^{n-1}).

    Can you simplify that?
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  3. #3
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    Re: how do you prove this using induction

    does it become f(n+1)=3f(n)+10f(n-1)<5^(n+1)
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  4. #4
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    Re: how do you prove this using induction

    It's basic arithmetic: factor 5^{n} out of 3(5^n)+ 10(5^{n-1}). What is left?
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