To find: if the series converges absolutely, converges conditionally or diverges.
Answer to Problem 26E
The series
Explanation of Solution
Given information:
The given series is
Formula used:
Ratio test is used.
Calculation:
Series converges absolutely.
Test for absolute convergence: The nth-Term Test
Here,
Apply L’ Hospital's rule,
Hence, series converges. Thus,
Now, calculate truncation error
Alternating Series Test (Leibniz’s theorem):
The series
Converges if all the three of the following conditions are satisfied:
1. Each
2.
3.
Here,
Hence,
Since,
Thus,
Now,
Apply L’ Hospital's rule,
Hence, it satisfies all condition of test.
The Alternating Series Estimation Theorem:
If the alternating series
Hence,
Truncation error after 99th term is less than
Conclusion:
The series
Chapter 10 Solutions
Calculus: Graphical, Numerical, Algebraic
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