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Write the sum in expanded form. E an where a, =2 and a, +1 = 2an n=0 3 E a, = 0 n=0 (Do not simplify.)

Write the sum in expanded form. E an where a, =2 and a, +1 = 2an n=0 3 E a, = 0 n=0 (Do not simplify.)

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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**Instructions:** Write the sum in expanded form. \[ \sum_{{n=0}}^{3} a_n \quad \text{where} \quad a_0 = 2 \quad \text{and} \quad a_{n+1} = 2a_n \] \[ \sum_{{n=0}}^{3} a_n = \text{[ ]} \quad (\text{Do not simplify.}) \] **Explanation:** You're asked to calculate and expand the sum \(\sum_{{n=0}}^{3} a_n\) given the conditions that \(a_0 = 2\) and each subsequent term \(a_{n+1}\) is twice the previous term \(a_n\). To solve this, you would start by finding each \(a_n\): - \(a_0 = 2\) - \(a_1 = 2a_0 = 4\) - \(a_2 = 2a_1 = 8\) - \(a_3 = 2a_2 = 16\) Then, you'll write each term explicitly in the sum, without simplifying: \[2 + 4 + 8 + 16\]
Transcribed Image Text:**Instructions:** Write the sum in expanded form. \[ \sum_{{n=0}}^{3} a_n \quad \text{where} \quad a_0 = 2 \quad \text{and} \quad a_{n+1} = 2a_n \] \[ \sum_{{n=0}}^{3} a_n = \text{[ ]} \quad (\text{Do not simplify.}) \] **Explanation:** You're asked to calculate and expand the sum \(\sum_{{n=0}}^{3} a_n\) given the conditions that \(a_0 = 2\) and each subsequent term \(a_{n+1}\) is twice the previous term \(a_n\). To solve this, you would start by finding each \(a_n\): - \(a_0 = 2\) - \(a_1 = 2a_0 = 4\) - \(a_2 = 2a_1 = 8\) - \(a_3 = 2a_2 = 16\) Then, you'll write each term explicitly in the sum, without simplifying: \[2 + 4 + 8 + 16\]
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