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.
The function is given by the table.
f: N\{1,2}-> N_{o}
__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?
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my opinions> It is ok 3) and 4). this function is the number of diagonals of a polygon with n sides, and
please help me about 1) and 2). how do I find the difference equation and functional equetion?
thank you!
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.