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Math Help - Help with mathematical induction

  1. #1
    Junior Member
    Joined
    Mar 2011
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    31

    Help with mathematical induction

    I have a series: a_{0},a_{1},a_{2}...


    a_{0}=1
    a_{n+1}=\frac{((a_{n})^{2}+9)}{6}\hspace{6} n\geq 1

    i want to find a explicit form for a_{n}
    and prove it with induction.


    i calculated some values to use:
    a_{1}=\frac{5}{3}
     a_{2}=\frac{53}{27}<br />


    i tried something like this:
    a_{n}=\frac{3n^4+n^2+1}{?}

    but im having a hard time finding a dominator that works with my values.

    Maybe im doing it all wrong

    regards mechaniac
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  2. #2
    Senior Member Sambit's Avatar
    Joined
    Oct 2010
    Posts
    355
    What do you mean by "explicit form"? If you want to get that expression in terms of n only, you may not get one. You already have a recursive relation between a_n and a_{n+1}; and this may be the most general form of the sequence.
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