To calculate: The series converges absolutely, converges conditionally, or diverges.
Answer to Problem 32E
The series converges conditionally.
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.
First examine the series
Can give a lower bound for the series
Determine whether the series
Let
By using the
Based on the previous two steps, by using the direct comparison test
Let check whether the series converges conditionally by using the alternating seriestest.
Since
Since
Finally,
Since
converges conditionally.
Therefore, the it conditionally converges.
Chapter 9 Solutions
CALCULUS-W/XL ACCESS
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