To find: The radius of convergence of this series.
Answer to Problem 59RE
The answer:
Explanation of Solution
Given information:
The equation is
Calculation:
Take the absolute value of the terms in the series since only use the Ratio Test for series with non-negative terms, and then look at the following limit:
The series converges absolutely if and only,
Therefore, the required radius of convergence of this series is
To find: The first three terms of this series to approximate
Answer to Problem 59RE
The answer:
Explanation of Solution
Given information:
The equation is
Calculation:
By use the given series and replace
Therefore, the required first three terms of this series to approximate
To find: The error involved in the approximation in part
Answer to Problem 59RE
The answer: The truncation error is less than
Explanation of Solution
Given information:
The equation is
Calculation:
The given series at
Is:
This is an alternating series and meets the requirements for the Alternating Series Error Bound; as a result, provide an upper bound for the truncation error.
According to the preceding step, the truncation error is less than the absolute value of the series' fourth term, i.e.
Therefore, the required truncation error is less than
Chapter 9 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
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