6. Let xn = n¹/ for n = N. a. Show that xn+1 < ï¸ if and only if (1+1/n)" < n, and infer that the inequality is valid for n > 3. (See Example 3.3.6.) Conclude that (in) is ultimately decreasing and that x = lim (xn) exists. b. Use the fact that the subsequence (2n) also converges to x to conclude that x = 1.

6. Let xn = n¹/ for n = N. a. Show that xn+1 < ï¸ if and only if (1+1/n)" < n, and infer that the inequality is valid for n > 3. (See Example 3.3.6.) Conclude that (in) is ultimately decreasing and that x = lim (xn) exists. b. Use the fact that the subsequence (2n) also converges to x to conclude that x = 1.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 23E

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