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Unformatted text preview: guage is not ”C”. CprE 310 Homework 3 14 Feb 2008, In class Problem 3.3 Prove the following for every integer n > 0. 1 2 + 2 2 + . . . + n 2 = n ( n + 1)(2 n + 1) 6 Problem 3.4 Prove the following for any integer n > 1. 1 1 · 2 + 1 2 · 3 + ··· + 1 ( n1) n = n1 n Problem 3.5 For any real number x > 0 and integer n ≥ 2, prove the following. (1 + x ) n > 1 + nx Problem 3.6 For any ±nite set S , let  S  denote the number of elements in S . For any positive integer n , for any collection of n ±nite sets S 1 , S 2 , . . . , S n , prove the following.  S 1 ∪ S 2 ∪ ··· ∪ S n  ≤  S 1  +  S 2  + . . . +  S n  2...
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 Spring '08
 Srikanta
 Natural number, following logical expressions, Theoretical Foundations of Computer Engg

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