To calculate: The series converges absolutely, converges conditionally, or diverges.
Answer to Problem 24E
The series converges absolutely, and the truncation error is less than
Explanation of Solution
Given information:
Calculation:
Let examine whether the series converges absolutely. If it does not, let use other tests in order to determine conditional convergence. The bound for the truncation error can be determined by using the Alternating Series Bound Theorem.
First let examine the series
Since
The truncation error can be determined by using the Alternating Series Bound Theorem. Based on this, the error after 99 terms is less than
Thus
Therefore, the series converges absolutely, and the 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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