(a)
To find: The geometric series in the form
(a)
Answer to Problem 39E
The geometric series is
Explanation of Solution
Given:
The value of
Concept used:
The mathematical expression of infinite geometric series in general is written as
The convergence test of series states that the geometric series converges if
Furthermore, the convergence test of geometric series also ensures that the convergent infinite geometric series
Calculation:
The infinite geometric series
Substitute 2 for a and 5 for S in the equation
Further simplify the above equation.
Therefore, the value of
Substitute 2 for a and
Here, the initial term is 2 and each sequential term is multiplied by
Therefore, the geometric series is
Conclusion:
Thus, the geometric series is
(b)
To find: The geometric series in the form
(b)
Answer to Problem 39E
The geometric series is
Explanation of Solution
Given:
The value of
Concept used:
The mathematical expression of infinite geometric series in general is written as
The convergence test of series states that the geometric series converges if
Furthermore, the convergence test of geometric series also ensures that the convergent infinite geometric series
Calculation:
The infinite geometric series
Substitute
Further simplify the above equation.
Therefore, the value of
Substitute 2 for a and
Here, the initial term is 2 and each sequential term is multiplied by
Therefore, the geometric series is
Conclusion:
Thus, the geometric series is
Chapter 10 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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