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Math Help - How do give the recursive form for a certain function?

  1. #1
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    How do give the recursive form for a certain function?

    I only have the explanation for linear homogeneous ones. I don't know how to do these:

    Give a recursive form (including bases) for the following functions:
    a. f(n) = 2 + (-1)^n
    b. f(n) = n(n+1)
    c. f(n) = 2n - 2
    d. f(n) = n^2 – n
    e. f(n) = 3^n + n⋅3^n

    If someone could explain one or two it would help alot.

    Thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by thename1000 View Post
    I only have the explanation for linear homogeneous ones. I don't know how to do these:

    Give a recursive form (including bases) for the following functions:
    a. f(n) = 2 + (-1)^n
    f(n)-f(n-1)=(-1)^n-(-1)^{n-1}=(-1)^n+(-1)^n=2 (-1)^n

    and take it from there

    CB
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by thename1000 View Post
    I
    d. f(n) = n^2 – n
    f(n)=n^2-n

    f(n-1)=n^2-3n+2

    f(n-2)=n^2-5n+4

    so:

    f(n-2)-2f(n-1)=(n^2-5n+4)-2(n^2-3n+2)=-n^2+n=-f(n)

    CB
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