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Math Help - Power series

  1. #1
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    Kongsberg
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    Power series

    Hello, a question


    Show by induction that if
    (N +1) an_ +1 + a_n-1 = 0 for all odd numbers n +1 ≥ 2 and a_0 = 1, then a_2N = (((-1) ^n))*((1/((2^n)*n!))
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  2. #2
    MHF Contributor

    Joined
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    Re: Power series

    I take it you mean (n+1)a_{n+1}+ a_{n-1}= 0 (If you don't want to use Latex, use parentheses: (n+1)a_(n+1)+ a_(n-1)= 0.
    And I think you mean a_{2n}= \frac{(-1)^n}{n!2^n}
    (a_(2n)= (-1)^n/(n!2^n))
    Please do not mix "n" and "N"!

    Now, do you know what induction is? If so, what have you tried to do and where do you have a problem?
    Have you checked that, when n= 1, a_2= 1/2?
    Thanks from topsquark
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  3. #3
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    Kongsberg
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    Re: Power series

    Ja, i will try to use parentes, because i do not know how to use Latex

    The question is to proof by induction that the first stammene is correctly which os equal zero?
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