Concept explainers
a.
To prove whether the sequence is monotone or not.
a.
Explanation of Solution
Given:
Calculation:
Consider the sequence
Then
The monotonic sequence should either be increasing or decreasing.
Since, the given sequence
Therefore the sequence
b.
To prove whether the sequence is monotone or not.
b.
Explanation of Solution
Given:
Calculation:
Consider the sequence
Then
The monotonic sequence should either be increasing or decreasing.
Since, the given sequence
Therefore the sequence
c.
To prove whether the sequence is monotone or not.
c.
Explanation of Solution
Given:
Calculation:
Consider the sequence
The monotonic sequence should either be increasing or decreasing.
Since, the given sequence
Therefore the sequence
d.
To prove whether the sequence is monotone or not.
d.
Explanation of Solution
Given:
Calculation:
Consider the sequence
Then
The monotonic sequence should either be increasing or decreasing.
Since, the given sequence
Therefore the sequence
e.
To prove whether the sequence is monotone or not.
e.
Explanation of Solution
Given:
Calculation:
Consider the sequence
The monotonic sequence should either be increasing or decreasing.
Since, the given sequence
Therefore the sequence
f.
To prove whether the sequence is monotone or not.
f.
Explanation of Solution
Given:
Calculation:
Consider the sequence
Then
The monotonic sequence should either be increasing or decreasing.
Since, the given sequence
Therefore the sequence
g.
To prove whether the sequence is monotone or not.
g.
Explanation of Solution
Given:
Calculation:
Consider the sequence
Then
The monotonic sequence should either be increasing or decreasing.
Since, the given sequence
Therefore the sequence
h.
To prove whether the sequence is monotone or not.
h.
Explanation of Solution
Given:
Calculation:
Consider the sequence
Then
The monotonic sequence should either be increasing or decreasing.
Since, the given sequence
Therefore the sequence
i.
To prove whether the sequence is monotone or not.
i.
Explanation of Solution
Given:
Calculation:
Consider the sequence
Then
The monotonic sequence should either be increasing or decreasing.
Since, the given sequence
Therefore the sequence
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Chapter 7 Solutions
A Transition to Advanced Mathematics
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