Please help me with these questions. I am having trouble understanding what to do. Please show all your work on paperSUBJECT: Discrete mathematicsThank you 1. Prove thatVk 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)}.

The first question is asking to prove that the sum of the kth powers of the first n natural numbers…

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 and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Please help me with these questions. I am having trouble understanding what to do. Please show all your work on paper

SUBJECT: Discrete mathematics

Thank you

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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