(1) When n=3, it can be known from plane geometry that the sum of the internal angles of the triangle is equal to 180, (n-2) 180 = (3-2) 180,

So this proposition holds when n=3.

(2) If n=k(k≥3), the proposition holds, that is, the sum of the internal angles of the k polygon is equal to (k-2) 180. As shown in the figure, connect A 1Ak to get A 1 on the k side.

A2…AK and triangle A 1A2Ak+ 1

Because the sum of the internal angles of the K polygon is equal to (k-2) 180 and the sum of the internal angles of the triangle is equal to 180, it can be seen from the figure that the sum of the internal angles of the k+ 1 polygon is (k-2) 180+080 =.

[(k+ 1)-2] 180 .

That is to say, if the n=k proposition holds, then the n=k+ 1 proposition also holds.

From (1)(2), we know that this proposition holds for any positive integer.