Find a simple expression for the following sum(no sums remaining): ΣΣ T(n) = 8-18-1 1-0 n-1
Find a simple expression for the following sum(no sums remaining): ΣΣ T(n) = 8-18-1 1-0 n-1
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Question
Transcribed Image Text:Find a simple expression for the following sum(no sums remaining):
του – ΣΣ
=
H - 1
Expert Solution
Step 1
We can simplify the expression as follows:
T(n) = ∑ᵢ₌₀ⁿ₋₁ ∑ⱼ₌₀ⁿ₋₁ (n-1)
We can rearrange the summation to obtain:
T(n) = ∑ᵢ₌₀ⁿ₋₁ ∑ⱼ₌₀ⁿ₋₁ (n-1)
= ∑ᵢ₌₀ⁿ₋₁ [(n-1) ∑ⱼ₌₀ⁿ₋₁ 1]
= ∑ᵢ₌₀ⁿ₋₁ [(n-1) × n]
= (n-1) × n × ∑ᵢ₌₀ⁿ₋₁ 1
= (n-1) × n × n
= n³ - n²
Step by step
Solved in 2 steps
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