To find:A geometric series for the function
Answer to Problem 56E
The geometric series including
Explanation of Solution
Given:
The function is
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 given function is
The given function fits the formula for infinite geometric series
The values are obtained as
Write the mathematical expression of infinite geometric series in this form
The nth term formula for the given function can be expressed as follows:
Here, the initial term is
Therefore, the geometric series including
The convergence test of geometric series states that the geometric series converges if
Therefore, the value of
Find the interval of convergence with
Therefore, the interval of convergence is
Conclusion:
Thus, the geometric series including
Chapter 10 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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