Chapter 11.1, Problem 62E

### Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Chapter
Section

### Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

# Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the sequence is convergent, guess the value of the limit from the graph and then prove your guess. (See the margin note on page 739 for advice on graphing sequences.) a n = 1 ⋅ 3 ⋅ 5 ⋅ … ⋅ ( 2 n − 1 ) n !

To determine

To decide:

a) The sequence converges or diverges

b) If it converges, find the limit

Explanation

1) Concept:

By observing the graph, identify whether the sequence is convergent or divergent, and also identify the limit if sequence is convergent

2) Definition:

Convergent: If limnan exists then the sequence is called convergent

Divergent: If limnan does not exist then the sequence is called divergent

3) Given:

an=1·3·5··2n-1n!

4) Calculation:

Consider the given sequence,

an=1·3·5··2n-1n!

To find first few terms of sequence,

a1=11=1

a2=1·31·2=1.5

a3=1·3·51·2·3=2.5

a4=1·3·5·71·2·3·4=4

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