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1. Prove that Vk € N, 1k + 2k + ... + nk € © (n²+1). 2. Suppose that the functions f1, f2, 91, 92: N→R20 are such that f₁ = O(g₁) and f₂ = O(92). Prove that (fi + ƒ2) € (max{91, 92}). Here (f1f2)(n) = f1(n) + f2(n) and max{91, 92}(n) = max{91(n), 92(n)}.

1. Prove that Vk € N, 1k + 2k + ... + nk € © (n²+1). 2. Suppose that the functions f1, f2, 91, 92: N→R20 are such that f₁ = O(g₁) and f₂ = O(92). Prove that (fi + ƒ2) € (max{91, 92}). Here (f1f2)(n) = f1(n) + f2(n) and max{91, 92}(n) = max{91(n), 92(n)}.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 49RE
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1. Prove that Vk € N, 1k + 2k + ... + nk € © (n²+1). 2. Suppose that the functions f1, f2, 91, 92: N→R20 are such that f₁ = O(g₁) and f₂ = O(92). Prove that (fi + ƒ2) € (max{91, 92}). Here (f1f2)(n) = f1(n) + f2(n) and max{91, 92}(n) = max{91(n), 92(n)}.
Transcribed Image Text:1. Prove that Vk € N, 1k + 2k + ... + nk € © (n²+1). 2. Suppose that the functions f1, f2, 91, 92: N→R20 are such that f₁ = O(g₁) and f₂ = O(92). Prove that (fi + ƒ2) € (max{91, 92}). Here (f1f2)(n) = f1(n) + f2(n) and max{91, 92}(n) = max{91(n), 92(n)}.
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