Prove by induction that a polygon with n angles has Mn = (n-3)n/2 diagonals.
We assume that the formula Mn+1=Mn +n - 1 is correct.
The Attempt at a Solution
First of all I checked if the 1st formula is correct for n=3 (a triangle): (3-3)*3/2=0. Correct.
Second, I set Mn+1 = ((n+1)-3)(n+1)/2 = (n2-n-2)/2. This is what I'm supposed to get if I use formula number 2.
This is what I got: Mn+1=Mn +n - 1 = ((n-3)n/2) +n - 1 = ((n+1)-3)(n+1)/2 = (n2-n-2)/2
So basically I finished the proof.. But problem is I don't understand what I did. I understand the concept of induction, but I don't know how I went through http://simple.wikipedia.org/wiki/Mathematical_induction" [Broken]:
3. Assume that for some value n, the statement is true. This is called the induction step.
4. Show that the statement is true for the next value, n+1.
Also please note that I have trouble understanding how to do step 3 and 4 in general, not just with this problem.
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