Consider the following sequence x₁ = √₁, x₂ = √1 + √I, x3 = √1+√₁+√₁ Evaluate lim xn (No credit for decimal answers- n→∞0 1+√5 answer must be exact, such as etc. 2

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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### Problem Statement

**Consider the following sequence:**

\[ x_1 = \sqrt{1}, \quad x_2 = \sqrt{1 + \sqrt{1}}, \quad x_3 = \sqrt{1 + \sqrt{1 + \sqrt{1}}} \]

**Evaluate** \(\lim_{{n \to \infty}} x_n\) **(No credit for decimal answers—the answer must be exact, such as** \(\frac{1 + \sqrt{5}}{2}\)**, etc.)**
Transcribed Image Text:### Problem Statement **Consider the following sequence:** \[ x_1 = \sqrt{1}, \quad x_2 = \sqrt{1 + \sqrt{1}}, \quad x_3 = \sqrt{1 + \sqrt{1 + \sqrt{1}}} \] **Evaluate** \(\lim_{{n \to \infty}} x_n\) **(No credit for decimal answers—the answer must be exact, such as** \(\frac{1 + \sqrt{5}}{2}\)**, etc.)**
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