1. Prove that Vk Є N, 1k+2k + ·+n²² € © (nk+1). 2. Suppose that the functions f₁, f2, 91, 92 : N → R≥º are such that ƒ1 € ☹(91) and ƒ2 € е(92). Prove that (fi + ƒ2) € ©(max{91, 92}). Here (f1f2)(n) = fi(n) + f2(n) and max{91, 92}(n) = max{91(n), 92(n)}.
1. Prove that Vk Є N, 1k+2k + ·+n²² € © (nk+1). 2. Suppose that the functions f₁, f2, 91, 92 : N → R≥º are such that ƒ1 € ☹(91) and ƒ2 € е(92). Prove that (fi + ƒ2) € ©(max{91, 92}). Here (f1f2)(n) = fi(n) + f2(n) and max{91, 92}(n) = max{91(n), 92(n)}.
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 Є N, 1k+2k + ·+n²² € © (nk+1).
2. Suppose that the functions f₁, f2, 91, 92 : N → R≥º are such that ƒ1 € ☹(91) and ƒ2 € е(92).
Prove that (fi + ƒ2) € ©(max{91, 92}).
Here (f1f2)(n) = fi(n) + f2(n) and max{91, 92}(n) = max{91(n), 92(n)}.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5354a32c-ee07-469b-96d5-42a00c955615%2Ffc678778-e4a2-4925-9548-7ec8f77545b2%2F49omnc7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Prove that
Vk Є N, 1k+2k + ·+n²² € © (nk+1).
2. Suppose that the functions f₁, f2, 91, 92 : N → R≥º are such that ƒ1 € ☹(91) and ƒ2 € е(92).
Prove that (fi + ƒ2) € ©(max{91, 92}).
Here (f1f2)(n) = fi(n) + f2(n) and max{91, 92}(n) = max{91(n), 92(n)}.
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