Extended Principle of Mathematical Induction The Extended Principle of Mathematical Induction states that if Conditions I and II hold, that is, (I) A statement is true for a natural number j. (II) If the statement is true for some natural number then it is also true for the next natural number then the statement is true for all natural numbers Use the Extended Principle of Mathematical Induction to show that the number of diagonals in a convex polygon of n sides is 12n1n - 32.

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