• Feb 6th 2013, 02:05 PM
feferon11
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?

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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 $f(n)=\frac{n\cdot(n-3)}{2}$

thank you!
• Feb 6th 2013, 03:30 PM
emakarov
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.
• Feb 6th 2013, 11:11 PM
feferon11
Re: About the one functional equation
Quote:

Originally Posted by emakarov
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.