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Unformatted text preview: a + b ) n as ( n i ) . ( a + b ) n = ± n ² a n + ± n 1 ² a n1 b + ± n 2 ² a n2 b 2 + ··· + ± n n1 ² ab n1 + ± n n ² b n or ( a + b ) n = n X i =0 ± n i ² a ni b i From the proof in the class we know that coeﬃcients ( n i ) satisfy ± n + 1 ² = ± n ² , ± n + 1 n + 1 ² = ± n n ² , and for 1 ≤ i ≤ n ± n + 1 i ² = ± n i1 ² + ± n i ² Problem 4. Prove that n X i =0 ± n i ² = 2 n n X i =0 (1) i ± n i ² = 0 Problem 5. Prove, using mathematical induction that ± n 1 ² + 2 ± n 2 ² + 3 ± n 3 ² + ··· + n ± n n ² = n 2 n1 2...
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This note was uploaded on 10/13/2010 for the course MATH 311W taught by Professor Mullen during the Spring '08 term at Penn State.
 Spring '08
 MULLEN
 Math, Mathematical Induction

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