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Math Help - About the one functional equation

  1. #1
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    About the one functional equation

    The function is given by the table.
    f: N\{1,2}-> No

    __n_| 3 | 4 | 5 | 6 | 07 | 08 | 09 | 10 |...
    f(n) | 0 | 2 | 5 | 9 | 14 | 20 | 27 | 35 | ...

    1) which functional equation characterizes this function?
    2) solve this difference equation.
    3) express this function in an explicit form
    4) what is this function of the planimetry?

    -------------------------------------------
    my opinions> It is ok 3) and 4). this function is the number of diagonals of a polygon with n sides, and f(n)=\frac{n\cdot(n-3)}{2}

    please help me about 1) and 2). how do I find the difference equation and functional equetion?

    thank you!
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  2. #2
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    Re: About the one functional equation

    The difference equation should be of the form f(n + 1) = f(n) + ... Draw a square with two diagonals, then add another point outside to create a pentagon. See how many diagonals you need to add? Try to extend this observation to the general case.
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  3. #3
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    Re: About the one functional equation

    Quote Originally Posted by emakarov View Post
    The difference equation should be of the form f(n + 1) = f(n) + ... Draw a square with two diagonals, then add another point outside to create a pentagon....
    Hmm, thank you very well...it is OK. I get> f(n+1)=f(n)+n-1 Nice.


    i will try to solwe it now...

    And, one more question:
    I need something else for the my seminar. Can we theoreticaly find some other problems related to the essential meaning of this function?

    Ty.
    Last edited by feferon11; February 6th 2013 at 11:21 PM.
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