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a²n+1 Exercise 3.2: Prove lim nxn! to explain the reasoning of why this is true. Hints: can be writtin as a2n+1 n! = 0, where a is a fixed positive integer. Be sure a. (a²)n n! 1. Show 2. Write the Maclaurin series for e. Recall that the Maclaurin series for e converges for all r. So, in particular, a times the Maclaurin series for e converges for x = =a² 3. Now, apply the fact that if en converges, then lim cn = 0 84x n=0

a²n+1 Exercise 3.2: Prove lim nxn! to explain the reasoning of why this is true. Hints: can be writtin as a2n+1 n! = 0, where a is a fixed positive integer. Be sure a. (a²)n n! 1. Show 2. Write the Maclaurin series for e. Recall that the Maclaurin series for e converges for all r. So, in particular, a times the Maclaurin series for e converges for x = =a² 3. Now, apply the fact that if en converges, then lim cn = 0 84x n=0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 50E
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Exercise 3.2: Prove lim a²n+1 1. Show a²n+1 n! n→∞n! to explain the reasoning of why this is true. Hints: can be writtin as a. 2. Write the Maclaurin series for e. Recall that the Maclaurin series for e converges for all x. So, in particular, a times the Maclaurin series for e converges for r = a² = = 0, where a is a fixed positive integer. Be sure n=0 n! 3. Now, apply the fact that if en converges, then lim cn = 0 Cn n4x
Transcribed Image Text:Exercise 3.2: Prove lim a²n+1 1. Show a²n+1 n! n→∞n! to explain the reasoning of why this is true. Hints: can be writtin as a. 2. Write the Maclaurin series for e. Recall that the Maclaurin series for e converges for all x. So, in particular, a times the Maclaurin series for e converges for r = a² = = 0, where a is a fixed positive integer. Be sure n=0 n! 3. Now, apply the fact that if en converges, then lim cn = 0 Cn n4x
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