This exercise uses one or more of the following results from Section 5.2. Exercise 5.2.10: For every integer n 2 1, 12 + 22 + + 02 = n(n + 1)(2n + 1) 6 n(n + 1) Exercise 5.2.11: For every integer n 2 1, 13 + 23 + -. + n3 = 2 Theorem 5.2.1: For every integer n 2 1, 1 + 2 +- +n= n(n + 1) Theorem 5.2.2: For any real number rexcept 1, and any integer n 2 0, - --1 r- 1 -0 Theorem on Polynomial Orders: If m is any integer with m 2 0 and ao, a, a,., am are real numbers with a, > 0, then anm + am,nm -1 +... + a,n + a, is O(n"). Prove the following statement. 5 + 10 + 15 + 20 + + 5n is O(n2). Proof: We get )(+ +2+3*** 5 + 10 + 15 + 20 + + 5n = = 51 by-Select--- %3! which is a polynomial of degree 1. So, by 5 + 10 + 15 + 20 + 25 + - + 5n is 0 n --Select--

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