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Write the sum without sigma notation and evaluate it. 4 2) > 2 cos k k = 1 A) 2 cos + 2 cos -2 +/2 4 B) 2 cos T + 2 cos --1 + /2 + 2 cos + 2 cos 4 + 2 cos+ 2 cos+ 2 cos --2•3+Z + 2 cos+2 cos+ 2 cos =3.2 C) 2 cos 7 + 2 cos 4 TO = 3 +/2 4

Write the sum without sigma notation and evaluate it. 4 2) > 2 cos k k = 1 A) 2 cos + 2 cos -2 +/2 4 B) 2 cos T + 2 cos --1 + /2 + 2 cos + 2 cos 4 + 2 cos+ 2 cos+ 2 cos --2•3+Z + 2 cos+2 cos+ 2 cos =3.2 C) 2 cos 7 + 2 cos 4 TO = 3 +/2 4

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Educational Content: Evaluating a Sum Without Sigma Notation** **Problem:** Write the sum without sigma notation and evaluate it. \[ 2) \quad \sum_{k=1}^{4} 2 \cos \frac{\pi}{k} \] **Options:** A) \[ 2 \cos \pi + 2 \cos \frac{\pi}{4} = -2 + \sqrt{2} \] B) \[ 2 \cos \pi + 2 \cos \frac{\pi}{2} + 2 \cos \frac{\pi}{3} + 2 \cos \frac{\pi}{4} = -1 + \sqrt{2} \] C) \[ 2 \cos \pi + 2 \cos \frac{\pi}{2} + 2 \cos \frac{\pi}{3} + 2 \cos \frac{\pi}{4} = -2 + \sqrt{3} + \sqrt{2} \] D) \[ 2 \cos \pi + 2 \cos \frac{\pi}{2} + 2 \cos \frac{\pi}{3} + 2 \cos \frac{\pi}{4} = 3 + \sqrt{2} \] **Solution Explanation:** To solve this problem, expand the sum: \[ \sum_{k=1}^{4} 2 \cos \frac{\pi}{k} = 2 \cos \pi + 2 \cos \frac{\pi}{2} + 2 \cos \frac{\pi}{3} + 2 \cos \frac{\pi}{4} \] Calculate each component: - \( 2 \cos \pi \) - \( 2 \cos \frac{\pi}{2} \) - \( 2 \cos \frac{\pi}{3} \) - \( 2 \cos \frac{\pi}{4} \) Then substitute the cosine values to find the total sum.
Transcribed Image Text:**Educational Content: Evaluating a Sum Without Sigma Notation** **Problem:** Write the sum without sigma notation and evaluate it. \[ 2) \quad \sum_{k=1}^{4} 2 \cos \frac{\pi}{k} \] **Options:** A) \[ 2 \cos \pi + 2 \cos \frac{\pi}{4} = -2 + \sqrt{2} \] B) \[ 2 \cos \pi + 2 \cos \frac{\pi}{2} + 2 \cos \frac{\pi}{3} + 2 \cos \frac{\pi}{4} = -1 + \sqrt{2} \] C) \[ 2 \cos \pi + 2 \cos \frac{\pi}{2} + 2 \cos \frac{\pi}{3} + 2 \cos \frac{\pi}{4} = -2 + \sqrt{3} + \sqrt{2} \] D) \[ 2 \cos \pi + 2 \cos \frac{\pi}{2} + 2 \cos \frac{\pi}{3} + 2 \cos \frac{\pi}{4} = 3 + \sqrt{2} \] **Solution Explanation:** To solve this problem, expand the sum: \[ \sum_{k=1}^{4} 2 \cos \frac{\pi}{k} = 2 \cos \pi + 2 \cos \frac{\pi}{2} + 2 \cos \frac{\pi}{3} + 2 \cos \frac{\pi}{4} \] Calculate each component: - \( 2 \cos \pi \) - \( 2 \cos \frac{\pi}{2} \) - \( 2 \cos \frac{\pi}{3} \) - \( 2 \cos \frac{\pi}{4} \) Then substitute the cosine values to find the total sum.
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