Concept explainers
(a)
To find: The sum of the given geometric sequence.
(a)
Answer to Problem 9T
The sum of the given geometric sequence is
Explanation of Solution
Given:
The given sequence is
Formula used:
For an infinite geometric series in the form,
Where, a is the first term and r is the common ratio of the sequence.
Calculation:
For an infinite geometric series in the form,
Compare the given sequence is
The value of the term
For geometric ratio
The value of geometric ratio
As, in the geometric sequence
Substitute
Further simplify of above equation,
Thus, the sum of the given geometric sequence is
(b)
To find: The sum of the given geometric sequence.
(b)
Answer to Problem 9T
The sum of the given geometric sequence is
Explanation of Solution
Given:
The given sequence is
Definition used:
For an infinite geometric series in the form,
Where, a is the first term and r is the common ratio of the sequence.
Calculation:
For an infinite geometric series in the form,
Compare the given sequence is
The value of the term
For geometric ratio
The value of geometric ratio
As, in the geometric sequence
Substitute
Multiply and divide the above equation with
Thus, the sum of the given geometric sequence is
Chapter 12 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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