The Extended Principle of Mathematical Induction states that if Conditions I and II hold, that is, (I)
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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 k ≥ j, then it is also true for the next natural number k + 1.
then the statement is true for all natural numbers ≥ j. Use the Extended Principle of Mathematical Induction to show that the number of diagonals in a convex polygon of n sides is 1/2n(n - 3).
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