To calculate: The series converges absolutely, converges conditionally, or diverges.
Answer to Problem 23E
The series is conditionally converges,
Explanation of Solution
Given information:
Calculation:
Alternating series test
The limit of the terms approaches zero.
Each successive term (without the sign) is smaller than the previous term.
So it converges.
To test for absolute convergence, drop the (-1) part, as the rest is positive. Separate the fraction
The original series converges and it doesn't converge absolutely, so it conditionally converges.
Using the alternating series estimation theorem, the truncation error after 99 terms is less than the value of the 100th term.
Therefore, the series is conditionally converges,
Chapter 9 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
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