Whether the series converges conditionally, converges absolutely, or diverges and bound for truncation error after 99 terms.
Answer to Problem 25E
The series is conditionally convergent.
Truncation error after 99 terms is
Explanation of Solution
Given information:
The series is alternating.
Thus,
We need to check for absolute convergence by considering the series of absolute values:
Now,
Use integral test to determine whether the series converges or not.
Let
The function
Now,
Determine whether the following integral converges or not:
Since the integral diverges, the series of absolute values diverges by the Integral Test and the series
Now,
Use Leibniz Test to check the conditional convergence.
Let
Then
And
Therefore,
The series is conditionally convergent.
Then
Truncation error after 99 terms:
Chapter 10 Solutions
Calculus: Graphical, Numerical, Algebraic
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