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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)}.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help me with the following questions below. I am not understanding what to do. Please show all your work on paper. Please try to complete both questions provided in the image below. Thank you so much

 
 
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)}.
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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