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## Homework Statement

Prove by induction that a polygon with n angles has M

_{n}= (n-3)n/2 diagonals.

## Homework Equations

We assume that the formula M

_{n+1}=M

_{n}+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 M

_{n+1}= ((n+1)-3)(n+1)/2 = (n

^{2}-n-2)/2. This is what I'm supposed to get if I use formula number 2.

This is what I got: M

_{n+1}=M

_{n}+n - 1 = ((n-3)n/2) +n - 1 = ((n+1)-3)(n+1)/2 = (n

^{2}-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.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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