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Unformatted text preview: (b) Induction Hypothesis. n 1 X i =1 i 2 = 2( n 1) 3 + 3( n 1) 2 + ( n 1) 6 . (c) Induction Step. n X i =1 i 2 = n 1 X i =1 i 2 + n 2 = 2( n 1) 3 + 3( n 1) 2 + ( n 1) 6 + n 2 = 2 n 3 6 n 2 + 6 n 2 + 3 n 2 6 n + 3 + n 1 6 + n 2 = 2 n 3 + 3 n 2 + n 6 . Thus, the theorem is proved by mathematical induction. 2.19 Proof : (a) Base case. For n = 1 , 1 / 2 = 1 1 / 2 = 1 / 2 . Thus, the formula is correct for the base case. (b) Induction Hypothesis. n 1 X i =1 1 2 i = 1 1 2 n 1 ....
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 Fall '08
 BELL,D

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