1. Prove that Vk Є N, 1k+2k + ·+nk € © (nk+1). 2. Suppose that the functions f₁, f2, 91, 92 : N → R≥º are such that ƒ1 € ☹(91) and ƒ2 € ☹(92). Prove that (fi + ƒ2) € ©(max{91, 92}). Here (f1f2)(n) = fi(n) + ƒ₂(n) and max{91, 92}(n) = max{91(n), 92(n)}.
1. Prove that Vk Є N, 1k+2k + ·+nk € © (nk+1). 2. Suppose that the functions f₁, f2, 91, 92 : N → R≥º are such that ƒ1 € ☹(91) and ƒ2 € ☹(92). Prove that (fi + ƒ2) € ©(max{91, 92}). Here (f1f2)(n) = fi(n) + ƒ₂(n) and max{91, 92}(n) = max{91(n), 92(n)}.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.1: Polynomial Functions Of Degree Greater Than
Problem 55E
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Transcribed Image Text:1. Prove that
Vk Є N, 1k+2k + ·+nk € © (nk+1).
2. Suppose that the functions f₁, f2, 91, 92 : N → R≥º are such that ƒ1 € ☹(91) and ƒ2 € ☹(92).
Prove that (fi + ƒ2) € ©(max{91, 92}).
Here (f1f2)(n) = fi(n) + ƒ₂(n) and max{91, 92}(n) = max{91(n), 92(n)}.
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