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Unformatted text preview: n + 1) (by the induction hypothesis P ( n )) = n ( n + 1) + 2( n + 1) 2 = ( n + 2)( n + 1) 2 = ( n + 1)(( n + 1) + 1) 2 . Then P ( n + 1) follows by the transitivity of equality. Since we proved this by assuming P ( n ), we have P ( n ) = ⇒ P ( n + 1). Since n was arbitrary, we have ∀ n ( P ( n ) = ⇒ P ( n + 1)) Since we proved P (0) and ∀ n ( P ( n ) = ⇒ P ( n + 1)), the statement ∀ nP ( n ) follows by the principle of Mathematical Induction, and the theorem follows. 1...
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This note was uploaded on 12/13/2011 for the course MHF 4102 taught by Professor Mitchelle during the Fall '11 term at University of Florida.
 Fall '11
 Mitchelle

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